cola Report for Ritz_ALL

Date: 2019-12-26 18:30:36 CET, cola version: 1.3.2

Summary

First the variable is renamed to res_list.

res_list = rl

All available functions which can be applied to this res_list object:

res_list

#> A 'ConsensusPartitionList' object with 24 methods.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#>   Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#>   Number of partitions are tried for k = 2, 3, 4, 5, 6.
#>   Performed in total 30000 partitions by row resampling.
#> 
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#>  [1] "cola_report"           "collect_classes"       "collect_plots"         "collect_stats"        
#>  [5] "colnames"              "functional_enrichment" "get_anno_col"          "get_anno"             
#>  [9] "get_classes"           "get_matrix"            "get_membership"        "get_stats"            
#> [13] "is_best_k"             "is_stable_k"           "ncol"                  "nrow"                 
#> [17] "rownames"              "show"                  "suggest_best_k"        "test_to_known_factors"
#> [21] "top_rows_heatmap"      "top_rows_overlap"     
#> 
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]

The call of run_all_consensus_partition_methods() was:

#> run_all_consensus_partition_methods(data = m, mc.cores = 4, anno = anno)

Dimension of the input matrix:

mat = get_matrix(res_list)
dim(mat)

#> [1] 11993   128

Density distribution

The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.

library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list), 
    col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
    mc.cores = 4)

plot of chunk density-heatmap

Suggest the best k

Folowing table shows the best k (number of partitions) for each combination of top-value methods and partition methods. Clicking on the method name in the table goes to the section for a single combination of methods.

The cola vignette explains the definition of the metrics used for determining the best number of partitions.

suggest_best_k(res_list)
The best k 1-PAC Mean silhouette Concordance Optional k
SD:skmeans 4 1.000 0.965 0.987 **
CV:skmeans 4 1.000 0.955 0.983 **
MAD:skmeans 4 1.000 0.958 0.983 **
ATC:pam 2 1.000 0.968 0.981 **
SD:mclust 4 0.972 0.945 0.975 **
ATC:kmeans 3 0.953 0.922 0.947 **
CV:mclust 4 0.942 0.936 0.971 * 2
CV:NMF 4 0.942 0.939 0.973 *
ATC:skmeans 3 0.915 0.886 0.954 * 2
MAD:mclust 4 0.906 0.930 0.966 *
SD:NMF 4 0.906 0.922 0.966 *
MAD:NMF 4 0.902 0.898 0.952 *
MAD:pam 4 0.899 0.885 0.953
CV:pam 4 0.893 0.882 0.952
SD:pam 4 0.881 0.868 0.948
ATC:mclust 2 0.859 0.909 0.947
MAD:kmeans 4 0.838 0.909 0.924
ATC:NMF 2 0.830 0.910 0.962
SD:kmeans 4 0.782 0.929 0.912
CV:kmeans 4 0.746 0.896 0.897
ATC:hclust 3 0.618 0.763 0.884
CV:hclust 5 0.528 0.602 0.689
MAD:hclust 3 0.328 0.663 0.785
SD:hclust 3 0.306 0.620 0.767

**: 1-PAC > 0.95, *: 1-PAC > 0.9

CDF of consensus matrices

Cumulative distribution function curves of consensus matrix for all methods.

collect_plots(res_list, fun = plot_ecdf)

plot of chunk collect-plots

Consensus heatmap

Consensus heatmaps for all methods. (What is a consensus heatmap?)

collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)

plot of chunk tab-collect-consensus-heatmap-1

Membership heatmap

Membership heatmaps for all methods. (What is a membership heatmap?)

collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)

plot of chunk tab-collect-membership-heatmap-1

Signature heatmap

Signature heatmaps for all methods. (What is a signature heatmap?)

Note in following heatmaps, rows are scaled.

collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)

plot of chunk tab-collect-get-signatures-1

Statistics table

The statistics used for measuring the stability of consensus partitioning. (How are they defined?)

get_stats(res_list, k = 2)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      2 0.387           0.735       0.860          0.437 0.556   0.556
#> CV:NMF      2 0.422           0.746       0.873          0.449 0.532   0.532
#> MAD:NMF     2 0.459           0.721       0.880          0.448 0.545   0.545
#> ATC:NMF     2 0.830           0.910       0.962          0.494 0.502   0.502
#> SD:skmeans  2 0.599           0.829       0.923          0.491 0.497   0.497
#> CV:skmeans  2 0.689           0.886       0.939          0.494 0.497   0.497
#> MAD:skmeans 2 0.801           0.880       0.949          0.501 0.500   0.500
#> ATC:skmeans 2 1.000           0.972       0.988          0.504 0.496   0.496
#> SD:mclust   2 0.761           0.958       0.963          0.396 0.614   0.614
#> CV:mclust   2 1.000           0.983       0.992          0.390 0.614   0.614
#> MAD:mclust  2 0.524           0.919       0.907          0.391 0.607   0.607
#> ATC:mclust  2 0.859           0.909       0.947          0.430 0.567   0.567
#> SD:kmeans   2 0.501           0.822       0.873          0.377 0.622   0.622
#> CV:kmeans   2 0.421           0.765       0.851          0.372 0.630   0.630
#> MAD:kmeans  2 0.358           0.822       0.864          0.417 0.614   0.614
#> ATC:kmeans  2 0.544           0.745       0.888          0.439 0.514   0.514
#> SD:pam      2 0.524           0.837       0.899          0.431 0.586   0.586
#> CV:pam      2 0.452           0.582       0.746          0.457 0.497   0.497
#> MAD:pam     2 0.400           0.775       0.824          0.480 0.497   0.497
#> ATC:pam     2 1.000           0.968       0.981          0.298 0.703   0.703
#> SD:hclust   2 0.786           0.915       0.949          0.333 0.674   0.674
#> CV:hclust   2 0.707           0.902       0.934          0.337 0.693   0.693
#> MAD:hclust  2 0.460           0.864       0.919          0.360 0.674   0.674
#> ATC:hclust  2 0.356           0.732       0.830          0.418 0.514   0.514

Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.

collect_stats(res_list, k = 2)

plot of chunk tab-collect-stats-from-consensus-partition-list-1

Partition from all methods

Collect partitions from all methods:

collect_classes(res_list, k = 2)

plot of chunk tab-collect-classes-from-consensus-partition-list-1

Top rows overlap

Overlap of top rows from different top-row methods:

top_rows_overlap(res_list, top_n = 1000, method = "euler")

plot of chunk tab-top-rows-overlap-by-euler-1

Also visualize the correspondance of rankings between different top-row methods:

top_rows_overlap(res_list, top_n = 1000, method = "correspondance")

plot of chunk tab-top-rows-overlap-by-correspondance-1

Heatmaps of the top rows:

top_rows_heatmap(res_list, top_n = 1000)

plot of chunk tab-top-rows-heatmap-1

Test to known annotations

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res_list, k = 2)

#>               n sex(p) age(p)    BT(p) k
#> SD:NMF      114  0.718 0.3924 1.13e-02 2
#> CV:NMF      117  0.944 0.6656 2.63e-03 2
#> MAD:NMF     104  0.532 0.5699 9.69e-04 2
#> ATC:NMF     122  0.669 0.1273 5.88e-01 2
#> SD:skmeans  119  0.848 0.8802 1.01e-06 2
#> CV:skmeans  124  0.608 0.9057 2.83e-07 2
#> MAD:skmeans 121  0.555 0.7912 2.66e-06 2
#> ATC:skmeans 127  0.569 0.3674 4.55e-01 2
#> SD:mclust   128  0.329 0.1726 3.06e-23 2
#> CV:mclust   128  0.329 0.1726 3.06e-23 2
#> MAD:mclust  127  0.364 0.1643 4.90e-23 2
#> ATC:mclust  125  0.320 0.8934 5.48e-02 2
#> SD:kmeans   122  0.235 0.8313 1.58e-01 2
#> CV:kmeans   122  0.235 0.8313 1.58e-01 2
#> MAD:kmeans  128  0.448 0.4314 6.90e-02 2
#> ATC:kmeans  115  0.499 0.5622 3.80e-01 2
#> SD:pam      124  0.349 0.0488 9.78e-21 2
#> CV:pam       85  0.553 0.1205 1.49e-01 2
#> MAD:pam     127  0.745 0.2305 4.02e-01 2
#> ATC:pam     126  1.000 0.8240 4.74e-01 2
#> SD:hclust   127  0.255 0.7826 3.01e-01 2
#> CV:hclust   125  0.334 0.9533 3.34e-01 2
#> MAD:hclust  124  0.350 0.9908 2.88e-01 2
#> ATC:hclust  118  0.787 0.0829 8.83e-01 2

Results for each method

SD:hclust

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'hclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk SD-hclust-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk SD-hclust-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.786           0.915       0.949         0.3333 0.674   0.674
#> 3 3 0.306           0.620       0.767         0.7742 0.684   0.532
#> 4 4 0.459           0.585       0.711         0.2048 0.851   0.606
#> 5 5 0.547           0.608       0.729         0.0865 0.950   0.812
#> 6 6 0.645           0.558       0.702         0.0502 0.972   0.879

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 3

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2  0.0376      0.957 0.004 0.996
#> 01010     1  0.0938      0.903 0.988 0.012
#> 03002     2  0.0000      0.957 0.000 1.000
#> 04006     1  0.0000      0.902 1.000 0.000
#> 04007     2  0.0000      0.957 0.000 1.000
#> 04008     1  0.9775      0.411 0.588 0.412
#> 04010     1  0.0000      0.902 1.000 0.000
#> 04016     2  0.0672      0.957 0.008 0.992
#> 06002     2  0.2423      0.948 0.040 0.960
#> 08001     2  0.0000      0.957 0.000 1.000
#> 08011     2  0.0376      0.957 0.004 0.996
#> 08012     2  0.0938      0.956 0.012 0.988
#> 08018     2  0.2778      0.947 0.048 0.952
#> 08024     2  0.1633      0.954 0.024 0.976
#> 09008     1  0.6247      0.841 0.844 0.156
#> 09017     2  0.0938      0.957 0.012 0.988
#> 11005     2  0.0000      0.957 0.000 1.000
#> 12006     2  0.2043      0.953 0.032 0.968
#> 12007     2  0.0376      0.957 0.004 0.996
#> 12012     2  0.2043      0.952 0.032 0.968
#> 12019     2  0.0672      0.957 0.008 0.992
#> 12026     2  0.2603      0.947 0.044 0.956
#> 14016     2  0.2236      0.951 0.036 0.964
#> 15001     2  0.1843      0.952 0.028 0.972
#> 15004     2  0.3114      0.942 0.056 0.944
#> 15005     1  0.6247      0.841 0.844 0.156
#> 16004     1  0.9286      0.550 0.656 0.344
#> 16009     1  0.0000      0.902 1.000 0.000
#> 19005     1  0.9286      0.550 0.656 0.344
#> 20002     1  0.5842      0.852 0.860 0.140
#> 22009     2  0.4298      0.918 0.088 0.912
#> 22010     2  0.5059      0.901 0.112 0.888
#> 22011     2  0.0938      0.956 0.012 0.988
#> 22013     2  0.2423      0.949 0.040 0.960
#> 24001     2  0.0938      0.956 0.012 0.988
#> 24005     2  0.2043      0.953 0.032 0.968
#> 24008     2  0.1843      0.952 0.028 0.972
#> 24010     2  0.2043      0.953 0.032 0.968
#> 24011     2  0.1414      0.956 0.020 0.980
#> 24017     1  0.2778      0.901 0.952 0.048
#> 24018     2  0.9000      0.572 0.316 0.684
#> 24019     1  0.0000      0.902 1.000 0.000
#> 24022     2  0.0000      0.957 0.000 1.000
#> 25003     2  0.0376      0.957 0.004 0.996
#> 25006     1  0.0000      0.902 1.000 0.000
#> 26001     2  0.2423      0.948 0.040 0.960
#> 26003     2  0.0376      0.957 0.004 0.996
#> 26005     2  0.1184      0.956 0.016 0.984
#> 26008     1  0.0000      0.902 1.000 0.000
#> 27003     2  0.7299      0.790 0.204 0.796
#> 27004     2  0.0376      0.957 0.004 0.996
#> 28001     2  0.7883      0.741 0.236 0.764
#> 28003     2  0.4161      0.925 0.084 0.916
#> 28005     2  0.0376      0.957 0.004 0.996
#> 28006     2  0.4022      0.920 0.080 0.920
#> 28007     2  0.0000      0.957 0.000 1.000
#> 28019     1  0.5059      0.881 0.888 0.112
#> 28021     1  0.5059      0.881 0.888 0.112
#> 28023     2  0.2423      0.950 0.040 0.960
#> 28024     2  0.0000      0.957 0.000 1.000
#> 28028     2  0.0000      0.957 0.000 1.000
#> 28031     2  0.2423      0.950 0.040 0.960
#> 28032     2  0.0000      0.957 0.000 1.000
#> 28035     1  0.5059      0.881 0.888 0.112
#> 28036     2  0.0000      0.957 0.000 1.000
#> 28037     1  0.4298      0.891 0.912 0.088
#> 28042     2  0.3584      0.936 0.068 0.932
#> 28043     2  0.0000      0.957 0.000 1.000
#> 28044     2  0.6247      0.843 0.156 0.844
#> 28047     2  0.0672      0.957 0.008 0.992
#> 30001     1  0.5059      0.881 0.888 0.112
#> 31007     2  0.3114      0.942 0.056 0.944
#> 31011     2  0.0938      0.957 0.012 0.988
#> 33005     1  0.0000      0.902 1.000 0.000
#> 36001     1  0.2948      0.901 0.948 0.052
#> 36002     2  0.0000      0.957 0.000 1.000
#> 37013     2  0.2423      0.950 0.040 0.960
#> 43001     2  0.2603      0.949 0.044 0.956
#> 43004     2  0.7745      0.742 0.228 0.772
#> 43007     2  0.0376      0.957 0.004 0.996
#> 43012     2  0.2423      0.950 0.040 0.960
#> 48001     1  0.4298      0.892 0.912 0.088
#> 49006     2  0.0000      0.957 0.000 1.000
#> 57001     2  0.4161      0.924 0.084 0.916
#> 62001     2  0.6623      0.821 0.172 0.828
#> 62002     2  0.0938      0.957 0.012 0.988
#> 62003     2  0.9087      0.554 0.324 0.676
#> 63001     2  0.0376      0.957 0.004 0.996
#> 64001     2  0.0376      0.957 0.004 0.996
#> 64002     1  0.0000      0.902 1.000 0.000
#> 65005     2  0.0000      0.957 0.000 1.000
#> 68001     1  0.0000      0.902 1.000 0.000
#> 68003     2  0.0376      0.957 0.004 0.996
#> 84004     2  0.0000      0.957 0.000 1.000
#> LAL5      2  0.3879      0.931 0.076 0.924
#> 01003     2  0.2236      0.949 0.036 0.964
#> 01007     2  0.3879      0.925 0.076 0.924
#> 02020     2  0.4298      0.916 0.088 0.912
#> 04018     2  0.4022      0.922 0.080 0.920
#> 09002     2  0.0000      0.957 0.000 1.000
#> 10005     2  0.0000      0.957 0.000 1.000
#> 11002     2  0.0000      0.957 0.000 1.000
#> 12008     2  0.0000      0.957 0.000 1.000
#> 15006     1  0.0000      0.902 1.000 0.000
#> 16002     2  0.1843      0.952 0.028 0.972
#> 16007     2  0.0000      0.957 0.000 1.000
#> 17003     2  0.4298      0.916 0.088 0.912
#> 18001     2  0.0000      0.957 0.000 1.000
#> 19002     2  0.4022      0.922 0.080 0.920
#> 19008     2  0.0000      0.957 0.000 1.000
#> 19014     2  0.4298      0.916 0.088 0.912
#> 19017     2  0.0000      0.957 0.000 1.000
#> 20005     2  0.0000      0.957 0.000 1.000
#> 24006     2  0.4022      0.922 0.080 0.920
#> 26009     1  0.0000      0.902 1.000 0.000
#> 28008     2  0.0000      0.957 0.000 1.000
#> 28009     2  0.4022      0.922 0.080 0.920
#> 31015     2  0.0938      0.956 0.012 0.988
#> 37001     2  0.4022      0.922 0.080 0.920
#> 43006     2  0.0000      0.957 0.000 1.000
#> 43015     2  0.0000      0.957 0.000 1.000
#> 44001     2  0.2236      0.949 0.036 0.964
#> 49004     2  0.0000      0.957 0.000 1.000
#> 56007     2  0.0000      0.957 0.000 1.000
#> 64005     2  0.0000      0.957 0.000 1.000
#> 65003     2  0.3584      0.930 0.068 0.932
#> 83001     2  0.4022      0.922 0.080 0.920
#> LAL4      2  0.4298      0.916 0.088 0.912

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-hclust-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-SD-hclust-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-SD-hclust-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-SD-hclust-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-hclust-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-SD-hclust-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-hclust-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>             n sex(p) age(p)    BT(p) k
#> SD:hclust 127  0.255  0.783 3.01e-01 2
#> SD:hclust  93  0.356  0.951 3.70e-11 3
#> SD:hclust 105  0.652  0.971 6.76e-17 4
#> SD:hclust 100  0.695  0.946 4.01e-14 5
#> SD:hclust  87  0.600  0.939 1.45e-09 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

SD:kmeans

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk SD-kmeans-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk SD-kmeans-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.501           0.822       0.873         0.3766 0.622   0.622
#> 3 3 0.720           0.742       0.870         0.6350 0.692   0.534
#> 4 4 0.782           0.929       0.912         0.1961 0.847   0.613
#> 5 5 0.765           0.729       0.836         0.0684 0.997   0.987
#> 6 6 0.738           0.547       0.738         0.0427 0.937   0.753

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2  0.8267      0.843 0.260 0.740
#> 01010     1  0.0000      0.902 1.000 0.000
#> 03002     2  0.7950      0.858 0.240 0.760
#> 04006     1  0.0000      0.902 1.000 0.000
#> 04007     2  0.7950      0.858 0.240 0.760
#> 04008     1  0.0000      0.902 1.000 0.000
#> 04010     1  0.0000      0.902 1.000 0.000
#> 04016     2  0.7950      0.858 0.240 0.760
#> 06002     2  0.8386      0.835 0.268 0.732
#> 08001     2  0.6887      0.880 0.184 0.816
#> 08011     2  0.8267      0.843 0.260 0.740
#> 08012     2  0.6887      0.880 0.184 0.816
#> 08018     2  0.7950      0.858 0.240 0.760
#> 08024     2  0.8327      0.839 0.264 0.736
#> 09008     1  0.0000      0.902 1.000 0.000
#> 09017     2  0.7056      0.878 0.192 0.808
#> 11005     2  0.6887      0.880 0.184 0.816
#> 12006     2  0.8267      0.843 0.260 0.740
#> 12007     2  0.8267      0.843 0.260 0.740
#> 12012     2  0.8267      0.843 0.260 0.740
#> 12019     2  0.8267      0.843 0.260 0.740
#> 12026     1  0.9358      0.292 0.648 0.352
#> 14016     1  0.9358      0.292 0.648 0.352
#> 15001     2  0.8386      0.835 0.268 0.732
#> 15004     2  0.6887      0.880 0.184 0.816
#> 15005     1  0.1414      0.887 0.980 0.020
#> 16004     1  0.0000      0.902 1.000 0.000
#> 16009     1  0.0000      0.902 1.000 0.000
#> 19005     1  0.4022      0.826 0.920 0.080
#> 20002     1  0.0000      0.902 1.000 0.000
#> 22009     2  0.8267      0.843 0.260 0.740
#> 22010     2  0.6801      0.880 0.180 0.820
#> 22011     2  0.7950      0.858 0.240 0.760
#> 22013     2  0.8386      0.835 0.268 0.732
#> 24001     2  0.7950      0.858 0.240 0.760
#> 24005     2  0.6887      0.880 0.184 0.816
#> 24008     2  0.8016      0.855 0.244 0.756
#> 24010     2  0.7950      0.858 0.240 0.760
#> 24011     2  0.8267      0.843 0.260 0.740
#> 24017     1  0.0000      0.902 1.000 0.000
#> 24018     1  0.2948      0.856 0.948 0.052
#> 24019     1  0.0000      0.902 1.000 0.000
#> 24022     2  0.6801      0.880 0.180 0.820
#> 25003     2  0.7950      0.858 0.240 0.760
#> 25006     1  0.0000      0.902 1.000 0.000
#> 26001     1  0.9286      0.317 0.656 0.344
#> 26003     2  0.6887      0.880 0.184 0.816
#> 26005     2  0.8386      0.835 0.268 0.732
#> 26008     1  0.0000      0.902 1.000 0.000
#> 27003     2  0.6887      0.880 0.184 0.816
#> 27004     2  0.6887      0.880 0.184 0.816
#> 28001     2  0.7376      0.873 0.208 0.792
#> 28003     2  0.6973      0.879 0.188 0.812
#> 28005     2  0.6887      0.880 0.184 0.816
#> 28006     2  0.6887      0.880 0.184 0.816
#> 28007     2  0.6887      0.880 0.184 0.816
#> 28019     1  0.0000      0.902 1.000 0.000
#> 28021     1  0.0000      0.902 1.000 0.000
#> 28023     2  0.6887      0.880 0.184 0.816
#> 28024     2  0.6887      0.880 0.184 0.816
#> 28028     2  0.6801      0.880 0.180 0.820
#> 28031     2  0.7602      0.868 0.220 0.780
#> 28032     2  0.6801      0.880 0.180 0.820
#> 28035     1  0.0000      0.902 1.000 0.000
#> 28036     2  0.6801      0.880 0.180 0.820
#> 28037     1  0.0000      0.902 1.000 0.000
#> 28042     2  0.6801      0.880 0.180 0.820
#> 28043     2  0.6887      0.880 0.184 0.816
#> 28044     2  0.6887      0.880 0.184 0.816
#> 28047     2  0.6887      0.880 0.184 0.816
#> 30001     1  0.0000      0.902 1.000 0.000
#> 31007     2  0.6887      0.880 0.184 0.816
#> 31011     2  0.6887      0.880 0.184 0.816
#> 33005     1  0.0000      0.902 1.000 0.000
#> 36001     1  0.0000      0.902 1.000 0.000
#> 36002     2  0.7950      0.858 0.240 0.760
#> 37013     2  0.8267      0.843 0.260 0.740
#> 43001     1  0.9358      0.292 0.648 0.352
#> 43004     2  0.8267      0.843 0.260 0.740
#> 43007     2  0.6973      0.879 0.188 0.812
#> 43012     2  0.6887      0.880 0.184 0.816
#> 48001     1  0.0000      0.902 1.000 0.000
#> 49006     2  0.8267      0.843 0.260 0.740
#> 57001     2  0.6887      0.880 0.184 0.816
#> 62001     2  0.6887      0.880 0.184 0.816
#> 62002     2  0.6887      0.880 0.184 0.816
#> 62003     1  0.9686      0.118 0.604 0.396
#> 63001     2  0.7299      0.874 0.204 0.796
#> 64001     2  0.8267      0.843 0.260 0.740
#> 64002     1  0.0000      0.902 1.000 0.000
#> 65005     2  0.7950      0.858 0.240 0.760
#> 68001     1  0.0000      0.902 1.000 0.000
#> 68003     2  0.7950      0.858 0.240 0.760
#> 84004     2  0.6887      0.880 0.184 0.816
#> LAL5      2  0.6887      0.880 0.184 0.816
#> 01003     2  0.0000      0.803 0.000 1.000
#> 01007     2  0.0672      0.799 0.008 0.992
#> 02020     2  0.0672      0.799 0.008 0.992
#> 04018     2  0.0672      0.799 0.008 0.992
#> 09002     2  0.0000      0.803 0.000 1.000
#> 10005     2  0.0000      0.803 0.000 1.000
#> 11002     2  0.0000      0.803 0.000 1.000
#> 12008     2  0.0000      0.803 0.000 1.000
#> 15006     1  0.6801      0.721 0.820 0.180
#> 16002     2  0.0000      0.803 0.000 1.000
#> 16007     2  0.0376      0.801 0.004 0.996
#> 17003     2  0.9922     -0.218 0.448 0.552
#> 18001     2  0.0000      0.803 0.000 1.000
#> 19002     2  0.0672      0.799 0.008 0.992
#> 19008     2  0.0000      0.803 0.000 1.000
#> 19014     2  0.0672      0.799 0.008 0.992
#> 19017     2  0.0000      0.803 0.000 1.000
#> 20005     2  0.0000      0.803 0.000 1.000
#> 24006     2  0.0672      0.799 0.008 0.992
#> 26009     1  0.6801      0.721 0.820 0.180
#> 28008     2  0.0000      0.803 0.000 1.000
#> 28009     2  0.0672      0.799 0.008 0.992
#> 31015     2  0.0000      0.803 0.000 1.000
#> 37001     2  0.0672      0.799 0.008 0.992
#> 43006     2  0.0000      0.803 0.000 1.000
#> 43015     2  0.0000      0.803 0.000 1.000
#> 44001     2  0.0672      0.799 0.008 0.992
#> 49004     2  0.0000      0.803 0.000 1.000
#> 56007     2  0.0000      0.803 0.000 1.000
#> 64005     2  0.0672      0.799 0.008 0.992
#> 65003     2  0.0672      0.799 0.008 0.992
#> 83001     2  0.0672      0.799 0.008 0.992
#> LAL4      2  0.0672      0.799 0.008 0.992

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-kmeans-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-SD-kmeans-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-SD-kmeans-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-SD-kmeans-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-kmeans-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-SD-kmeans-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-kmeans-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>             n sex(p) age(p)    BT(p) k
#> SD:kmeans 122  0.235  0.831 1.58e-01 2
#> SD:kmeans  96  0.128  0.535 7.54e-14 3
#> SD:kmeans 126  0.163  0.703 2.24e-20 4
#> SD:kmeans 117  0.334  0.723 2.36e-18 5
#> SD:kmeans  74  0.536  0.929 1.98e-10 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

SD:skmeans**

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk SD-skmeans-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk SD-skmeans-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.599           0.829       0.923         0.4906 0.497   0.497
#> 3 3 0.748           0.870       0.928         0.3405 0.765   0.563
#> 4 4 1.000           0.965       0.987         0.1451 0.848   0.591
#> 5 5 0.852           0.760       0.879         0.0596 0.941   0.770
#> 6 6 0.798           0.646       0.796         0.0341 0.970   0.861

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     1  0.0376      0.928 0.996 0.004
#> 01010     1  0.0000      0.929 1.000 0.000
#> 03002     1  0.5629      0.790 0.868 0.132
#> 04006     1  0.0000      0.929 1.000 0.000
#> 04007     2  0.9710      0.467 0.400 0.600
#> 04008     1  0.0000      0.929 1.000 0.000
#> 04010     1  0.0000      0.929 1.000 0.000
#> 04016     1  0.9993     -0.129 0.516 0.484
#> 06002     1  0.0376      0.928 0.996 0.004
#> 08001     2  0.7219      0.808 0.200 0.800
#> 08011     1  0.0376      0.928 0.996 0.004
#> 08012     2  0.7219      0.808 0.200 0.800
#> 08018     1  0.1633      0.913 0.976 0.024
#> 08024     1  0.0376      0.928 0.996 0.004
#> 09008     1  0.0000      0.929 1.000 0.000
#> 09017     2  0.9087      0.634 0.324 0.676
#> 11005     2  0.7219      0.808 0.200 0.800
#> 12006     1  0.0376      0.928 0.996 0.004
#> 12007     1  0.0376      0.928 0.996 0.004
#> 12012     1  0.0376      0.928 0.996 0.004
#> 12019     1  0.0376      0.928 0.996 0.004
#> 12026     1  0.0000      0.929 1.000 0.000
#> 14016     1  0.0000      0.929 1.000 0.000
#> 15001     1  0.0376      0.928 0.996 0.004
#> 15004     2  0.2603      0.877 0.044 0.956
#> 15005     1  0.0000      0.929 1.000 0.000
#> 16004     1  0.0000      0.929 1.000 0.000
#> 16009     1  0.0000      0.929 1.000 0.000
#> 19005     1  0.0000      0.929 1.000 0.000
#> 20002     1  0.0000      0.929 1.000 0.000
#> 22009     1  0.0000      0.929 1.000 0.000
#> 22010     2  0.0376      0.889 0.004 0.996
#> 22011     1  1.0000     -0.173 0.504 0.496
#> 22013     1  0.0000      0.929 1.000 0.000
#> 24001     1  0.9998     -0.159 0.508 0.492
#> 24005     2  0.7219      0.808 0.200 0.800
#> 24008     1  0.0376      0.928 0.996 0.004
#> 24010     1  0.8955      0.455 0.688 0.312
#> 24011     1  0.0376      0.928 0.996 0.004
#> 24017     1  0.0000      0.929 1.000 0.000
#> 24018     1  0.0000      0.929 1.000 0.000
#> 24019     1  0.0000      0.929 1.000 0.000
#> 24022     2  0.7139      0.811 0.196 0.804
#> 25003     1  0.0376      0.928 0.996 0.004
#> 25006     1  0.0000      0.929 1.000 0.000
#> 26001     1  0.0000      0.929 1.000 0.000
#> 26003     2  0.7219      0.808 0.200 0.800
#> 26005     1  0.0376      0.928 0.996 0.004
#> 26008     1  0.0000      0.929 1.000 0.000
#> 27003     2  0.7299      0.807 0.204 0.796
#> 27004     2  0.7219      0.808 0.200 0.800
#> 28001     1  0.6531      0.737 0.832 0.168
#> 28003     2  0.0376      0.889 0.004 0.996
#> 28005     2  0.7219      0.808 0.200 0.800
#> 28006     2  0.7219      0.808 0.200 0.800
#> 28007     2  0.7219      0.808 0.200 0.800
#> 28019     1  0.0000      0.929 1.000 0.000
#> 28021     1  0.0000      0.929 1.000 0.000
#> 28023     2  0.7219      0.808 0.200 0.800
#> 28024     2  0.7219      0.808 0.200 0.800
#> 28028     2  0.0376      0.889 0.004 0.996
#> 28031     1  0.7299      0.687 0.796 0.204
#> 28032     2  0.0000      0.890 0.000 1.000
#> 28035     1  0.0000      0.929 1.000 0.000
#> 28036     2  0.6887      0.818 0.184 0.816
#> 28037     1  0.0000      0.929 1.000 0.000
#> 28042     2  0.0000      0.890 0.000 1.000
#> 28043     2  0.7219      0.808 0.200 0.800
#> 28044     2  0.7299      0.807 0.204 0.796
#> 28047     2  0.6438      0.827 0.164 0.836
#> 30001     1  0.0000      0.929 1.000 0.000
#> 31007     2  0.0376      0.889 0.004 0.996
#> 31011     2  0.7219      0.808 0.200 0.800
#> 33005     1  0.0000      0.929 1.000 0.000
#> 36001     1  0.0000      0.929 1.000 0.000
#> 36002     1  0.9996     -0.144 0.512 0.488
#> 37013     1  0.0000      0.929 1.000 0.000
#> 43001     1  0.0000      0.929 1.000 0.000
#> 43004     1  0.0000      0.929 1.000 0.000
#> 43007     2  0.9552      0.523 0.376 0.624
#> 43012     2  0.0000      0.890 0.000 1.000
#> 48001     1  0.0000      0.929 1.000 0.000
#> 49006     1  0.0376      0.928 0.996 0.004
#> 57001     2  0.1633      0.884 0.024 0.976
#> 62001     2  0.7299      0.807 0.204 0.796
#> 62002     2  0.7299      0.807 0.204 0.796
#> 62003     1  0.0000      0.929 1.000 0.000
#> 63001     2  0.9635      0.496 0.388 0.612
#> 64001     1  0.0376      0.928 0.996 0.004
#> 64002     1  0.0000      0.929 1.000 0.000
#> 65005     1  0.0376      0.928 0.996 0.004
#> 68001     1  0.0000      0.929 1.000 0.000
#> 68003     2  1.0000      0.177 0.496 0.504
#> 84004     2  0.7219      0.808 0.200 0.800
#> LAL5      2  0.0000      0.890 0.000 1.000
#> 01003     2  0.0000      0.890 0.000 1.000
#> 01007     2  0.0376      0.889 0.004 0.996
#> 02020     2  0.0376      0.889 0.004 0.996
#> 04018     2  0.0000      0.890 0.000 1.000
#> 09002     2  0.0000      0.890 0.000 1.000
#> 10005     2  0.0000      0.890 0.000 1.000
#> 11002     2  0.0000      0.890 0.000 1.000
#> 12008     2  0.0000      0.890 0.000 1.000
#> 15006     1  0.7219      0.708 0.800 0.200
#> 16002     2  0.0000      0.890 0.000 1.000
#> 16007     2  0.0000      0.890 0.000 1.000
#> 17003     1  0.9522      0.440 0.628 0.372
#> 18001     2  0.0000      0.890 0.000 1.000
#> 19002     2  0.0376      0.889 0.004 0.996
#> 19008     2  0.0000      0.890 0.000 1.000
#> 19014     2  0.0376      0.889 0.004 0.996
#> 19017     2  0.0000      0.890 0.000 1.000
#> 20005     2  0.0000      0.890 0.000 1.000
#> 24006     2  0.0376      0.889 0.004 0.996
#> 26009     1  0.7219      0.708 0.800 0.200
#> 28008     2  0.0000      0.890 0.000 1.000
#> 28009     2  0.0376      0.889 0.004 0.996
#> 31015     2  0.0000      0.890 0.000 1.000
#> 37001     2  0.0376      0.889 0.004 0.996
#> 43006     2  0.0000      0.890 0.000 1.000
#> 43015     2  0.0000      0.890 0.000 1.000
#> 44001     2  0.0000      0.890 0.000 1.000
#> 49004     2  0.0000      0.890 0.000 1.000
#> 56007     2  0.0000      0.890 0.000 1.000
#> 64005     2  0.0376      0.889 0.004 0.996
#> 65003     2  0.0376      0.889 0.004 0.996
#> 83001     2  0.0376      0.889 0.004 0.996
#> LAL4      2  0.0376      0.889 0.004 0.996

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-skmeans-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-SD-skmeans-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-SD-skmeans-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-SD-skmeans-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-skmeans-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-SD-skmeans-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-skmeans-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>              n sex(p) age(p)    BT(p) k
#> SD:skmeans 119  0.848  0.880 1.01e-06 2
#> SD:skmeans 127  0.146  0.909 7.57e-08 3
#> SD:skmeans 126  0.214  0.703 1.09e-20 4
#> SD:skmeans 109  0.347  0.840 3.71e-16 5
#> SD:skmeans  96  0.361  0.933 3.05e-11 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

SD:pam

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk SD-pam-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk SD-pam-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.524           0.837       0.899         0.4307 0.586   0.586
#> 3 3 0.456           0.599       0.803         0.5120 0.516   0.319
#> 4 4 0.881           0.868       0.948         0.1462 0.794   0.494
#> 5 5 0.859           0.791       0.908         0.0554 0.937   0.765
#> 6 6 0.804           0.619       0.793         0.0292 0.955   0.796

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     1  0.3274      0.889 0.940 0.060
#> 01010     1  0.0000      0.891 1.000 0.000
#> 03002     1  0.3274      0.889 0.940 0.060
#> 04006     1  0.0000      0.891 1.000 0.000
#> 04007     1  0.3274      0.889 0.940 0.060
#> 04008     1  0.0000      0.891 1.000 0.000
#> 04010     1  0.0000      0.891 1.000 0.000
#> 04016     1  0.0000      0.891 1.000 0.000
#> 06002     1  0.0000      0.891 1.000 0.000
#> 08001     1  0.7528      0.819 0.784 0.216
#> 08011     1  0.3274      0.889 0.940 0.060
#> 08012     1  0.3274      0.889 0.940 0.060
#> 08018     1  0.9896      0.124 0.560 0.440
#> 08024     1  0.0000      0.891 1.000 0.000
#> 09008     1  0.0000      0.891 1.000 0.000
#> 09017     1  0.7528      0.819 0.784 0.216
#> 11005     1  0.7528      0.819 0.784 0.216
#> 12006     1  0.1843      0.891 0.972 0.028
#> 12007     1  0.3274      0.889 0.940 0.060
#> 12012     1  0.3274      0.889 0.940 0.060
#> 12019     1  0.0000      0.891 1.000 0.000
#> 12026     1  0.0000      0.891 1.000 0.000
#> 14016     1  0.0000      0.891 1.000 0.000
#> 15001     1  0.0000      0.891 1.000 0.000
#> 15004     1  0.7528      0.819 0.784 0.216
#> 15005     1  0.0000      0.891 1.000 0.000
#> 16004     1  0.0000      0.891 1.000 0.000
#> 16009     1  0.0000      0.891 1.000 0.000
#> 19005     1  0.0000      0.891 1.000 0.000
#> 20002     1  0.0000      0.891 1.000 0.000
#> 22009     1  0.0000      0.891 1.000 0.000
#> 22010     2  0.8909      0.669 0.308 0.692
#> 22011     1  0.3274      0.889 0.940 0.060
#> 22013     1  0.0000      0.891 1.000 0.000
#> 24001     1  0.3274      0.889 0.940 0.060
#> 24005     1  0.7376      0.824 0.792 0.208
#> 24008     1  0.3114      0.889 0.944 0.056
#> 24010     1  0.7528      0.819 0.784 0.216
#> 24011     1  0.0000      0.891 1.000 0.000
#> 24017     1  0.0000      0.891 1.000 0.000
#> 24018     1  0.0000      0.891 1.000 0.000
#> 24019     1  0.4022      0.825 0.920 0.080
#> 24022     1  0.7528      0.819 0.784 0.216
#> 25003     1  0.0000      0.891 1.000 0.000
#> 25006     1  0.0000      0.891 1.000 0.000
#> 26001     1  0.0000      0.891 1.000 0.000
#> 26003     1  0.7528      0.819 0.784 0.216
#> 26005     1  0.0000      0.891 1.000 0.000
#> 26008     1  0.0000      0.891 1.000 0.000
#> 27003     1  0.7528      0.819 0.784 0.216
#> 27004     1  0.7528      0.819 0.784 0.216
#> 28001     1  0.9850      0.327 0.572 0.428
#> 28003     2  0.3584      0.853 0.068 0.932
#> 28005     1  0.7528      0.819 0.784 0.216
#> 28006     1  0.7528      0.819 0.784 0.216
#> 28007     1  0.7528      0.819 0.784 0.216
#> 28019     1  0.0000      0.891 1.000 0.000
#> 28021     1  0.0000      0.891 1.000 0.000
#> 28023     1  0.7528      0.819 0.784 0.216
#> 28024     1  0.7528      0.819 0.784 0.216
#> 28028     1  0.7528      0.819 0.784 0.216
#> 28031     1  0.4161      0.871 0.916 0.084
#> 28032     1  0.7528      0.819 0.784 0.216
#> 28035     1  0.0000      0.891 1.000 0.000
#> 28036     1  0.7528      0.819 0.784 0.216
#> 28037     1  0.0000      0.891 1.000 0.000
#> 28042     2  0.9323      0.292 0.348 0.652
#> 28043     1  0.7528      0.819 0.784 0.216
#> 28044     1  0.7528      0.819 0.784 0.216
#> 28047     1  0.7528      0.819 0.784 0.216
#> 30001     1  0.0000      0.891 1.000 0.000
#> 31007     1  0.6973      0.809 0.812 0.188
#> 31011     1  0.7528      0.819 0.784 0.216
#> 33005     1  0.0000      0.891 1.000 0.000
#> 36001     1  0.5178      0.778 0.884 0.116
#> 36002     1  0.3274      0.889 0.940 0.060
#> 37013     1  0.3274      0.889 0.940 0.060
#> 43001     1  0.0000      0.891 1.000 0.000
#> 43004     1  0.0000      0.891 1.000 0.000
#> 43007     1  0.3274      0.889 0.940 0.060
#> 43012     1  0.9635      0.572 0.612 0.388
#> 48001     1  0.0000      0.891 1.000 0.000
#> 49006     1  0.3274      0.889 0.940 0.060
#> 57001     1  0.4022      0.882 0.920 0.080
#> 62001     1  0.3584      0.887 0.932 0.068
#> 62002     1  0.7528      0.819 0.784 0.216
#> 62003     1  0.0000      0.891 1.000 0.000
#> 63001     1  0.7528      0.819 0.784 0.216
#> 64001     1  0.3274      0.889 0.940 0.060
#> 64002     1  0.0376      0.889 0.996 0.004
#> 65005     1  0.3431      0.888 0.936 0.064
#> 68001     1  0.0000      0.891 1.000 0.000
#> 68003     1  0.7528      0.819 0.784 0.216
#> 84004     1  0.7219      0.828 0.800 0.200
#> LAL5      2  0.9686      0.121 0.396 0.604
#> 01003     2  0.0000      0.859 0.000 1.000
#> 01007     2  0.7528      0.831 0.216 0.784
#> 02020     2  0.7528      0.831 0.216 0.784
#> 04018     2  0.0000      0.859 0.000 1.000
#> 09002     2  0.4690      0.854 0.100 0.900
#> 10005     2  0.2603      0.835 0.044 0.956
#> 11002     2  0.0000      0.859 0.000 1.000
#> 12008     2  0.7056      0.836 0.192 0.808
#> 15006     2  0.7528      0.831 0.216 0.784
#> 16002     2  0.0000      0.859 0.000 1.000
#> 16007     2  0.0000      0.859 0.000 1.000
#> 17003     2  0.7528      0.831 0.216 0.784
#> 18001     2  0.0000      0.859 0.000 1.000
#> 19002     2  0.7528      0.831 0.216 0.784
#> 19008     2  0.0000      0.859 0.000 1.000
#> 19014     2  0.7528      0.831 0.216 0.784
#> 19017     2  0.0000      0.859 0.000 1.000
#> 20005     2  0.0000      0.859 0.000 1.000
#> 24006     2  0.7528      0.831 0.216 0.784
#> 26009     2  0.7528      0.831 0.216 0.784
#> 28008     2  0.0000      0.859 0.000 1.000
#> 28009     2  0.6973      0.841 0.188 0.812
#> 31015     2  0.1843      0.861 0.028 0.972
#> 37001     2  0.7528      0.831 0.216 0.784
#> 43006     2  0.0000      0.859 0.000 1.000
#> 43015     2  0.6247      0.837 0.156 0.844
#> 44001     2  0.6801      0.842 0.180 0.820
#> 49004     2  0.0000      0.859 0.000 1.000
#> 56007     2  0.0000      0.859 0.000 1.000
#> 64005     2  0.7528      0.831 0.216 0.784
#> 65003     2  0.0000      0.859 0.000 1.000
#> 83001     2  0.7528      0.831 0.216 0.784
#> LAL4      2  0.3274      0.853 0.060 0.940

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-pam-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-SD-pam-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-SD-pam-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-SD-pam-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-pam-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-SD-pam-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-pam-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>          n sex(p) age(p)    BT(p) k
#> SD:pam 124  0.349 0.0488 9.78e-21 2
#> SD:pam  82  0.142 0.8614 8.76e-11 3
#> SD:pam 118  0.480 0.9675 2.87e-15 4
#> SD:pam 112  0.571 0.7498 1.27e-14 5
#> SD:pam  96  0.706 0.2353 2.07e-15 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

SD:mclust**

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'mclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk SD-mclust-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk SD-mclust-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.761           0.958       0.963         0.3963 0.614   0.614
#> 3 3 0.633           0.711       0.802         0.5851 0.726   0.554
#> 4 4 0.972           0.945       0.975         0.1850 0.899   0.709
#> 5 5 0.858           0.871       0.887         0.0331 0.991   0.966
#> 6 6 0.821           0.742       0.853         0.0388 0.920   0.699

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     1  0.0000      0.952 1.000 0.000
#> 01010     1  0.4690      0.941 0.900 0.100
#> 03002     1  0.0000      0.952 1.000 0.000
#> 04006     1  0.4690      0.941 0.900 0.100
#> 04007     1  0.0000      0.952 1.000 0.000
#> 04008     1  0.3584      0.942 0.932 0.068
#> 04010     1  0.4690      0.941 0.900 0.100
#> 04016     1  0.0376      0.953 0.996 0.004
#> 06002     1  0.0000      0.952 1.000 0.000
#> 08001     1  0.2043      0.958 0.968 0.032
#> 08011     1  0.0000      0.952 1.000 0.000
#> 08012     1  0.0000      0.952 1.000 0.000
#> 08018     1  0.0000      0.952 1.000 0.000
#> 08024     1  0.0000      0.952 1.000 0.000
#> 09008     1  0.4690      0.941 0.900 0.100
#> 09017     1  0.2043      0.958 0.968 0.032
#> 11005     1  0.0000      0.952 1.000 0.000
#> 12006     1  0.0000      0.952 1.000 0.000
#> 12007     1  0.0000      0.952 1.000 0.000
#> 12012     1  0.0000      0.952 1.000 0.000
#> 12019     1  0.0000      0.952 1.000 0.000
#> 12026     1  0.3431      0.943 0.936 0.064
#> 14016     1  0.0938      0.953 0.988 0.012
#> 15001     1  0.0000      0.952 1.000 0.000
#> 15004     1  0.2043      0.958 0.968 0.032
#> 15005     1  0.4690      0.941 0.900 0.100
#> 16004     1  0.4690      0.941 0.900 0.100
#> 16009     1  0.4690      0.941 0.900 0.100
#> 19005     1  0.4690      0.941 0.900 0.100
#> 20002     1  0.3584      0.942 0.932 0.068
#> 22009     1  0.0000      0.952 1.000 0.000
#> 22010     1  0.9129      0.623 0.672 0.328
#> 22011     1  0.0000      0.952 1.000 0.000
#> 22013     1  0.0000      0.952 1.000 0.000
#> 24001     1  0.0000      0.952 1.000 0.000
#> 24005     1  0.2043      0.958 0.968 0.032
#> 24008     1  0.0000      0.952 1.000 0.000
#> 24010     1  0.0000      0.952 1.000 0.000
#> 24011     1  0.0000      0.952 1.000 0.000
#> 24017     1  0.4690      0.941 0.900 0.100
#> 24018     1  0.4690      0.941 0.900 0.100
#> 24019     1  0.4690      0.941 0.900 0.100
#> 24022     1  0.2043      0.958 0.968 0.032
#> 25003     1  0.0000      0.952 1.000 0.000
#> 25006     1  0.4690      0.941 0.900 0.100
#> 26001     1  0.0000      0.952 1.000 0.000
#> 26003     1  0.2043      0.958 0.968 0.032
#> 26005     1  0.0000      0.952 1.000 0.000
#> 26008     1  0.4690      0.941 0.900 0.100
#> 27003     1  0.4690      0.941 0.900 0.100
#> 27004     1  0.2043      0.958 0.968 0.032
#> 28001     1  0.5059      0.932 0.888 0.112
#> 28003     1  0.4690      0.941 0.900 0.100
#> 28005     1  0.2043      0.958 0.968 0.032
#> 28006     1  0.2043      0.958 0.968 0.032
#> 28007     1  0.2043      0.958 0.968 0.032
#> 28019     1  0.4690      0.941 0.900 0.100
#> 28021     1  0.4690      0.941 0.900 0.100
#> 28023     1  0.2043      0.958 0.968 0.032
#> 28024     1  0.2043      0.958 0.968 0.032
#> 28028     1  0.2043      0.958 0.968 0.032
#> 28031     1  0.2043      0.958 0.968 0.032
#> 28032     1  0.4161      0.946 0.916 0.084
#> 28035     1  0.4690      0.941 0.900 0.100
#> 28036     1  0.2043      0.958 0.968 0.032
#> 28037     1  0.4690      0.941 0.900 0.100
#> 28042     1  0.5178      0.928 0.884 0.116
#> 28043     1  0.2043      0.958 0.968 0.032
#> 28044     1  0.2043      0.958 0.968 0.032
#> 28047     1  0.2043      0.958 0.968 0.032
#> 30001     1  0.4690      0.941 0.900 0.100
#> 31007     1  0.5059      0.932 0.888 0.112
#> 31011     1  0.2043      0.958 0.968 0.032
#> 33005     1  0.4690      0.941 0.900 0.100
#> 36001     1  0.4690      0.941 0.900 0.100
#> 36002     1  0.2043      0.958 0.968 0.032
#> 37013     1  0.2043      0.958 0.968 0.032
#> 43001     1  0.0000      0.952 1.000 0.000
#> 43004     1  0.4690      0.941 0.900 0.100
#> 43007     1  0.0000      0.952 1.000 0.000
#> 43012     1  0.4690      0.941 0.900 0.100
#> 48001     1  0.4690      0.941 0.900 0.100
#> 49006     1  0.0000      0.952 1.000 0.000
#> 57001     1  0.2043      0.958 0.968 0.032
#> 62001     1  0.2236      0.957 0.964 0.036
#> 62002     1  0.2043      0.958 0.968 0.032
#> 62003     1  0.4690      0.941 0.900 0.100
#> 63001     1  0.0000      0.952 1.000 0.000
#> 64001     1  0.0000      0.952 1.000 0.000
#> 64002     1  0.4690      0.941 0.900 0.100
#> 65005     1  0.0000      0.952 1.000 0.000
#> 68001     1  0.4690      0.941 0.900 0.100
#> 68003     1  0.0000      0.952 1.000 0.000
#> 84004     1  0.2043      0.958 0.968 0.032
#> LAL5      1  0.3879      0.949 0.924 0.076
#> 01003     2  0.0000      0.997 0.000 1.000
#> 01007     2  0.0000      0.997 0.000 1.000
#> 02020     2  0.0000      0.997 0.000 1.000
#> 04018     2  0.0000      0.997 0.000 1.000
#> 09002     2  0.0000      0.997 0.000 1.000
#> 10005     2  0.3114      0.954 0.056 0.944
#> 11002     2  0.0000      0.997 0.000 1.000
#> 12008     2  0.0000      0.997 0.000 1.000
#> 15006     2  0.1633      0.974 0.024 0.976
#> 16002     2  0.0000      0.997 0.000 1.000
#> 16007     2  0.0000      0.997 0.000 1.000
#> 17003     2  0.0000      0.997 0.000 1.000
#> 18001     2  0.0000      0.997 0.000 1.000
#> 19002     2  0.0000      0.997 0.000 1.000
#> 19008     2  0.0000      0.997 0.000 1.000
#> 19014     2  0.0000      0.997 0.000 1.000
#> 19017     2  0.0000      0.997 0.000 1.000
#> 20005     2  0.0000      0.997 0.000 1.000
#> 24006     2  0.0000      0.997 0.000 1.000
#> 26009     2  0.1633      0.974 0.024 0.976
#> 28008     2  0.0000      0.997 0.000 1.000
#> 28009     2  0.0000      0.997 0.000 1.000
#> 31015     2  0.0000      0.997 0.000 1.000
#> 37001     2  0.0000      0.997 0.000 1.000
#> 43006     2  0.0000      0.997 0.000 1.000
#> 43015     2  0.0000      0.997 0.000 1.000
#> 44001     2  0.0000      0.997 0.000 1.000
#> 49004     2  0.0000      0.997 0.000 1.000
#> 56007     2  0.0000      0.997 0.000 1.000
#> 64005     2  0.0000      0.997 0.000 1.000
#> 65003     2  0.0000      0.997 0.000 1.000
#> 83001     2  0.0000      0.997 0.000 1.000
#> LAL4      2  0.0000      0.997 0.000 1.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-mclust-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-SD-mclust-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-SD-mclust-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-SD-mclust-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-mclust-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-SD-mclust-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-mclust-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>             n sex(p) age(p)    BT(p) k
#> SD:mclust 128  0.329  0.173 3.06e-23 2
#> SD:mclust 113  0.141  0.343 9.05e-22 3
#> SD:mclust 127  0.108  0.599 5.41e-22 4
#> SD:mclust 124  0.151  0.650 1.03e-21 5
#> SD:mclust 116  0.538  0.853 5.08e-17 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

SD:NMF*

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'NMF' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk SD-NMF-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk SD-NMF-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.387           0.735       0.860         0.4366 0.556   0.556
#> 3 3 0.682           0.828       0.916         0.4674 0.689   0.489
#> 4 4 0.906           0.922       0.966         0.1701 0.826   0.550
#> 5 5 0.795           0.769       0.879         0.0653 0.898   0.627
#> 6 6 0.748           0.696       0.824         0.0330 0.980   0.900

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     1  0.9983    -0.2484 0.524 0.476
#> 01010     1  0.0000     0.8863 1.000 0.000
#> 03002     2  0.9427     0.6366 0.360 0.640
#> 04006     1  0.0000     0.8863 1.000 0.000
#> 04007     2  0.9710     0.5697 0.400 0.600
#> 04008     1  0.0000     0.8863 1.000 0.000
#> 04010     1  0.0000     0.8863 1.000 0.000
#> 04016     2  0.9460     0.6305 0.364 0.636
#> 06002     1  0.8813     0.4159 0.700 0.300
#> 08001     2  0.7219     0.7970 0.200 0.800
#> 08011     2  0.9993     0.3617 0.484 0.516
#> 08012     2  0.7219     0.7970 0.200 0.800
#> 08018     2  0.7528     0.7876 0.216 0.784
#> 08024     1  0.9427     0.2308 0.640 0.360
#> 09008     1  0.0000     0.8863 1.000 0.000
#> 09017     2  0.8144     0.7597 0.252 0.748
#> 11005     2  0.7219     0.7970 0.200 0.800
#> 12006     2  0.9909     0.4743 0.444 0.556
#> 12007     2  0.9881     0.4931 0.436 0.564
#> 12012     2  0.9944     0.4430 0.456 0.544
#> 12019     1  0.9988    -0.2629 0.520 0.480
#> 12026     1  0.0000     0.8863 1.000 0.000
#> 14016     1  0.0672     0.8801 0.992 0.008
#> 15001     1  0.4161     0.8079 0.916 0.084
#> 15004     2  0.7219     0.7970 0.200 0.800
#> 15005     1  0.0000     0.8863 1.000 0.000
#> 16004     1  0.0000     0.8863 1.000 0.000
#> 16009     1  0.0000     0.8863 1.000 0.000
#> 19005     1  0.0000     0.8863 1.000 0.000
#> 20002     1  0.0000     0.8863 1.000 0.000
#> 22009     2  0.9909     0.4744 0.444 0.556
#> 22010     2  0.0000     0.7892 0.000 1.000
#> 22011     2  0.9044     0.6897 0.320 0.680
#> 22013     1  0.4431     0.7988 0.908 0.092
#> 24001     2  0.9686     0.5771 0.396 0.604
#> 24005     2  0.7219     0.7970 0.200 0.800
#> 24008     2  0.9815     0.5289 0.420 0.580
#> 24010     2  0.9686     0.5772 0.396 0.604
#> 24011     1  0.9608     0.1412 0.616 0.384
#> 24017     1  0.0000     0.8863 1.000 0.000
#> 24018     1  0.0000     0.8863 1.000 0.000
#> 24019     1  0.0000     0.8863 1.000 0.000
#> 24022     2  0.5294     0.8016 0.120 0.880
#> 25003     2  0.9580     0.6048 0.380 0.620
#> 25006     1  0.0000     0.8863 1.000 0.000
#> 26001     1  0.0000     0.8863 1.000 0.000
#> 26003     2  0.7219     0.7970 0.200 0.800
#> 26005     1  0.7453     0.6171 0.788 0.212
#> 26008     1  0.0000     0.8863 1.000 0.000
#> 27003     2  0.6973     0.7993 0.188 0.812
#> 27004     2  0.7219     0.7970 0.200 0.800
#> 28001     2  0.7815     0.7768 0.232 0.768
#> 28003     2  0.6712     0.8008 0.176 0.824
#> 28005     2  0.7219     0.7970 0.200 0.800
#> 28006     2  0.7219     0.7970 0.200 0.800
#> 28007     2  0.7219     0.7970 0.200 0.800
#> 28019     1  0.0000     0.8863 1.000 0.000
#> 28021     1  0.0000     0.8863 1.000 0.000
#> 28023     2  0.7376     0.7927 0.208 0.792
#> 28024     2  0.7219     0.7970 0.200 0.800
#> 28028     2  0.4815     0.8009 0.104 0.896
#> 28031     2  0.9358     0.6482 0.352 0.648
#> 28032     2  0.0000     0.7892 0.000 1.000
#> 28035     1  0.0000     0.8863 1.000 0.000
#> 28036     2  0.4562     0.8001 0.096 0.904
#> 28037     1  0.0000     0.8863 1.000 0.000
#> 28042     2  0.0000     0.7892 0.000 1.000
#> 28043     2  0.7219     0.7970 0.200 0.800
#> 28044     2  0.7815     0.7763 0.232 0.768
#> 28047     2  0.7139     0.7980 0.196 0.804
#> 30001     1  0.0000     0.8863 1.000 0.000
#> 31007     2  0.7139     0.7980 0.196 0.804
#> 31011     2  0.7299     0.7949 0.204 0.796
#> 33005     1  0.0000     0.8863 1.000 0.000
#> 36001     1  0.0000     0.8863 1.000 0.000
#> 36002     2  0.9710     0.5697 0.400 0.600
#> 37013     2  0.9998     0.3371 0.492 0.508
#> 43001     1  0.0000     0.8863 1.000 0.000
#> 43004     1  0.6712     0.6809 0.824 0.176
#> 43007     2  0.7219     0.7970 0.200 0.800
#> 43012     2  0.6531     0.8012 0.168 0.832
#> 48001     1  0.0000     0.8863 1.000 0.000
#> 49006     2  0.9909     0.4742 0.444 0.556
#> 57001     2  0.7219     0.7970 0.200 0.800
#> 62001     2  0.9460     0.6343 0.364 0.636
#> 62002     2  0.8661     0.7254 0.288 0.712
#> 62003     1  0.0000     0.8863 1.000 0.000
#> 63001     2  0.7219     0.7970 0.200 0.800
#> 64001     1  0.9710     0.0748 0.600 0.400
#> 64002     1  0.0000     0.8863 1.000 0.000
#> 65005     2  0.9710     0.5697 0.400 0.600
#> 68001     1  0.0000     0.8863 1.000 0.000
#> 68003     2  0.9000     0.6947 0.316 0.684
#> 84004     2  0.7219     0.7970 0.200 0.800
#> LAL5      2  0.6048     0.8018 0.148 0.852
#> 01003     2  0.0000     0.7892 0.000 1.000
#> 01007     2  0.0000     0.7892 0.000 1.000
#> 02020     2  0.0000     0.7892 0.000 1.000
#> 04018     2  0.0000     0.7892 0.000 1.000
#> 09002     2  0.0000     0.7892 0.000 1.000
#> 10005     2  0.0000     0.7892 0.000 1.000
#> 11002     2  0.0000     0.7892 0.000 1.000
#> 12008     2  0.0000     0.7892 0.000 1.000
#> 15006     1  0.7219     0.6601 0.800 0.200
#> 16002     2  0.0000     0.7892 0.000 1.000
#> 16007     2  0.0000     0.7892 0.000 1.000
#> 17003     2  0.8081     0.4756 0.248 0.752
#> 18001     2  0.0000     0.7892 0.000 1.000
#> 19002     2  0.0000     0.7892 0.000 1.000
#> 19008     2  0.0000     0.7892 0.000 1.000
#> 19014     2  0.0000     0.7892 0.000 1.000
#> 19017     2  0.0000     0.7892 0.000 1.000
#> 20005     2  0.0000     0.7892 0.000 1.000
#> 24006     2  0.0000     0.7892 0.000 1.000
#> 26009     1  0.7219     0.6601 0.800 0.200
#> 28008     2  0.0000     0.7892 0.000 1.000
#> 28009     2  0.0000     0.7892 0.000 1.000
#> 31015     2  0.0000     0.7892 0.000 1.000
#> 37001     2  0.0000     0.7892 0.000 1.000
#> 43006     2  0.0000     0.7892 0.000 1.000
#> 43015     2  0.0000     0.7892 0.000 1.000
#> 44001     2  0.0000     0.7892 0.000 1.000
#> 49004     2  0.0000     0.7892 0.000 1.000
#> 56007     2  0.0000     0.7892 0.000 1.000
#> 64005     2  0.0000     0.7892 0.000 1.000
#> 65003     2  0.0000     0.7892 0.000 1.000
#> 83001     2  0.0000     0.7892 0.000 1.000
#> LAL4      2  0.0000     0.7892 0.000 1.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-NMF-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-SD-NMF-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-SD-NMF-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-SD-NMF-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-NMF-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-SD-NMF-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-NMF-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>          n sex(p) age(p)    BT(p) k
#> SD:NMF 114  0.718 0.3924 1.13e-02 2
#> SD:NMF 121  0.110 0.8444 1.45e-07 3
#> SD:NMF 125  0.244 0.5986 1.10e-18 4
#> SD:NMF 116  0.341 0.4134 2.03e-14 5
#> SD:NMF 107  0.182 0.0574 5.56e-14 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

CV:hclust

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'hclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk CV-hclust-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk CV-hclust-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.707           0.902       0.934         0.3374 0.693   0.693
#> 3 3 0.350           0.509       0.751         0.6318 0.692   0.557
#> 4 4 0.460           0.522       0.730         0.2542 0.842   0.646
#> 5 5 0.528           0.602       0.689         0.1004 0.858   0.604
#> 6 6 0.650           0.561       0.749         0.0523 0.958   0.825

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 5

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2  0.1414      0.938 0.020 0.980
#> 01010     1  0.2778      0.941 0.952 0.048
#> 03002     2  0.0376      0.937 0.004 0.996
#> 04006     1  0.1843      0.941 0.972 0.028
#> 04007     2  0.0376      0.937 0.004 0.996
#> 04008     2  0.8608      0.661 0.284 0.716
#> 04010     1  0.1843      0.941 0.972 0.028
#> 04016     2  0.0938      0.938 0.012 0.988
#> 06002     2  0.6438      0.843 0.164 0.836
#> 08001     2  0.0938      0.938 0.012 0.988
#> 08011     2  0.1414      0.938 0.020 0.980
#> 08012     2  0.1414      0.937 0.020 0.980
#> 08018     2  0.6247      0.860 0.156 0.844
#> 08024     2  0.6247      0.851 0.156 0.844
#> 09008     1  0.4298      0.928 0.912 0.088
#> 09017     2  0.0000      0.937 0.000 1.000
#> 11005     2  0.0376      0.937 0.004 0.996
#> 12006     2  0.3274      0.923 0.060 0.940
#> 12007     2  0.1414      0.938 0.020 0.980
#> 12012     2  0.6438      0.843 0.164 0.836
#> 12019     2  0.4815      0.898 0.104 0.896
#> 12026     2  0.6531      0.839 0.168 0.832
#> 14016     2  0.6438      0.843 0.164 0.836
#> 15001     2  0.5408      0.884 0.124 0.876
#> 15004     2  0.4298      0.911 0.088 0.912
#> 15005     1  0.4562      0.921 0.904 0.096
#> 16004     1  0.9170      0.530 0.668 0.332
#> 16009     1  0.1843      0.941 0.972 0.028
#> 19005     1  0.9170      0.530 0.668 0.332
#> 20002     2  0.9775      0.362 0.412 0.588
#> 22009     2  0.5294      0.887 0.120 0.880
#> 22010     2  0.2043      0.937 0.032 0.968
#> 22011     2  0.1414      0.937 0.020 0.980
#> 22013     2  0.6438      0.843 0.164 0.836
#> 24001     2  0.1414      0.937 0.020 0.980
#> 24005     2  0.0000      0.937 0.000 1.000
#> 24008     2  0.2043      0.935 0.032 0.968
#> 24010     2  0.1184      0.938 0.016 0.984
#> 24011     2  0.5294      0.887 0.120 0.880
#> 24017     1  0.4022      0.930 0.920 0.080
#> 24018     2  0.9491      0.458 0.368 0.632
#> 24019     1  0.1843      0.941 0.972 0.028
#> 24022     2  0.0000      0.937 0.000 1.000
#> 25003     2  0.4161      0.910 0.084 0.916
#> 25006     1  0.1843      0.941 0.972 0.028
#> 26001     2  0.6438      0.843 0.164 0.836
#> 26003     2  0.0000      0.937 0.000 1.000
#> 26005     2  0.5408      0.883 0.124 0.876
#> 26008     1  0.1843      0.941 0.972 0.028
#> 27003     2  0.1843      0.938 0.028 0.972
#> 27004     2  0.0376      0.937 0.004 0.996
#> 28001     2  0.4815      0.899 0.104 0.896
#> 28003     2  0.3431      0.923 0.064 0.936
#> 28005     2  0.0000      0.937 0.000 1.000
#> 28006     2  0.4815      0.899 0.104 0.896
#> 28007     2  0.0000      0.937 0.000 1.000
#> 28019     1  0.4161      0.931 0.916 0.084
#> 28021     1  0.4161      0.931 0.916 0.084
#> 28023     2  0.0000      0.937 0.000 1.000
#> 28024     2  0.0000      0.937 0.000 1.000
#> 28028     2  0.0000      0.937 0.000 1.000
#> 28031     2  0.0000      0.937 0.000 1.000
#> 28032     2  0.0000      0.937 0.000 1.000
#> 28035     1  0.4431      0.925 0.908 0.092
#> 28036     2  0.0376      0.937 0.004 0.996
#> 28037     1  0.3431      0.938 0.936 0.064
#> 28042     2  0.0938      0.938 0.012 0.988
#> 28043     2  0.0376      0.937 0.004 0.996
#> 28044     2  0.6148      0.850 0.152 0.848
#> 28047     2  0.0000      0.937 0.000 1.000
#> 30001     1  0.4161      0.931 0.916 0.084
#> 31007     2  0.4298      0.911 0.088 0.912
#> 31011     2  0.0000      0.937 0.000 1.000
#> 33005     1  0.1843      0.941 0.972 0.028
#> 36001     1  0.2423      0.942 0.960 0.040
#> 36002     2  0.1633      0.936 0.024 0.976
#> 37013     2  0.6343      0.846 0.160 0.840
#> 43001     2  0.3274      0.923 0.060 0.940
#> 43004     2  0.6531      0.829 0.168 0.832
#> 43007     2  0.2603      0.931 0.044 0.956
#> 43012     2  0.0000      0.937 0.000 1.000
#> 48001     1  0.3879      0.935 0.924 0.076
#> 49006     2  0.0938      0.938 0.012 0.988
#> 57001     2  0.1633      0.938 0.024 0.976
#> 62001     2  0.3584      0.912 0.068 0.932
#> 62002     2  0.0000      0.937 0.000 1.000
#> 62003     2  0.9686      0.381 0.396 0.604
#> 63001     2  0.0000      0.937 0.000 1.000
#> 64001     2  0.1414      0.938 0.020 0.980
#> 64002     1  0.1843      0.941 0.972 0.028
#> 65005     2  0.0938      0.938 0.012 0.988
#> 68001     1  0.1843      0.941 0.972 0.028
#> 68003     2  0.2778      0.928 0.048 0.952
#> 84004     2  0.0376      0.937 0.004 0.996
#> LAL5      2  0.3431      0.923 0.064 0.936
#> 01003     2  0.3431      0.931 0.064 0.936
#> 01007     2  0.2948      0.932 0.052 0.948
#> 02020     2  0.3431      0.931 0.064 0.936
#> 04018     2  0.3274      0.931 0.060 0.940
#> 09002     2  0.2043      0.929 0.032 0.968
#> 10005     2  0.1843      0.929 0.028 0.972
#> 11002     2  0.1843      0.929 0.028 0.972
#> 12008     2  0.3274      0.931 0.060 0.940
#> 15006     1  0.0672      0.929 0.992 0.008
#> 16002     2  0.3274      0.932 0.060 0.940
#> 16007     2  0.2043      0.929 0.032 0.968
#> 17003     2  0.3431      0.931 0.064 0.936
#> 18001     2  0.2043      0.930 0.032 0.968
#> 19002     2  0.3584      0.929 0.068 0.932
#> 19008     2  0.2043      0.929 0.032 0.968
#> 19014     2  0.3431      0.931 0.064 0.936
#> 19017     2  0.1843      0.929 0.028 0.972
#> 20005     2  0.1843      0.929 0.028 0.972
#> 24006     2  0.3274      0.931 0.060 0.940
#> 26009     1  0.0672      0.929 0.992 0.008
#> 28008     2  0.1843      0.929 0.028 0.972
#> 28009     2  0.3584      0.929 0.068 0.932
#> 31015     2  0.2948      0.933 0.052 0.948
#> 37001     2  0.3584      0.929 0.068 0.932
#> 43006     2  0.1843      0.929 0.028 0.972
#> 43015     2  0.3274      0.931 0.060 0.940
#> 44001     2  0.3431      0.931 0.064 0.936
#> 49004     2  0.2043      0.929 0.032 0.968
#> 56007     2  0.2043      0.929 0.032 0.968
#> 64005     2  0.3274      0.931 0.060 0.940
#> 65003     2  0.3584      0.929 0.068 0.932
#> 83001     2  0.3431      0.931 0.064 0.936
#> LAL4      2  0.3431      0.931 0.064 0.936

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-hclust-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-CV-hclust-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-CV-hclust-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-CV-hclust-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-hclust-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-CV-hclust-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-hclust-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>             n sex(p) age(p)    BT(p) k
#> CV:hclust 125  0.334  0.953 3.34e-01 2
#> CV:hclust  93  0.303  0.766 1.34e-05 3
#> CV:hclust  68  0.159  0.426 1.59e-03 4
#> CV:hclust  87  0.327  0.625 8.10e-14 5
#> CV:hclust  87  0.452  0.763 7.69e-13 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

CV:kmeans

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk CV-kmeans-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk CV-kmeans-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.421           0.765       0.851         0.3716 0.630   0.630
#> 3 3 0.727           0.782       0.836         0.6329 0.703   0.551
#> 4 4 0.746           0.896       0.897         0.2074 0.851   0.626
#> 5 5 0.766           0.710       0.833         0.0704 0.980   0.922
#> 6 6 0.726           0.594       0.768         0.0414 0.930   0.724

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2  0.9286     0.7457 0.344 0.656
#> 01010     1  0.0000     0.8742 1.000 0.000
#> 03002     2  0.8386     0.8247 0.268 0.732
#> 04006     1  0.0000     0.8742 1.000 0.000
#> 04007     2  0.8386     0.8247 0.268 0.732
#> 04008     1  0.0000     0.8742 1.000 0.000
#> 04010     1  0.0000     0.8742 1.000 0.000
#> 04016     2  0.8386     0.8247 0.268 0.732
#> 06002     2  0.9552     0.6961 0.376 0.624
#> 08001     2  0.7674     0.8446 0.224 0.776
#> 08011     2  0.9286     0.7457 0.344 0.656
#> 08012     2  0.8207     0.8315 0.256 0.744
#> 08018     2  0.8267     0.8294 0.260 0.740
#> 08024     2  0.9323     0.7401 0.348 0.652
#> 09008     1  0.0000     0.8742 1.000 0.000
#> 09017     2  0.7674     0.8446 0.224 0.776
#> 11005     2  0.7674     0.8446 0.224 0.776
#> 12006     2  0.8443     0.8217 0.272 0.728
#> 12007     2  0.9000     0.7794 0.316 0.684
#> 12012     2  0.9286     0.7457 0.344 0.656
#> 12019     2  0.9323     0.7401 0.348 0.652
#> 12026     1  0.9954    -0.2760 0.540 0.460
#> 14016     1  0.9954    -0.2760 0.540 0.460
#> 15001     2  0.9552     0.6961 0.376 0.624
#> 15004     2  0.7674     0.8446 0.224 0.776
#> 15005     1  0.0672     0.8670 0.992 0.008
#> 16004     1  0.0000     0.8742 1.000 0.000
#> 16009     1  0.0000     0.8742 1.000 0.000
#> 19005     1  0.7815     0.5294 0.768 0.232
#> 20002     1  0.0000     0.8742 1.000 0.000
#> 22009     2  0.9248     0.7508 0.340 0.660
#> 22010     2  0.7528     0.8434 0.216 0.784
#> 22011     2  0.8386     0.8247 0.268 0.732
#> 22013     2  0.9552     0.6961 0.376 0.624
#> 24001     2  0.8386     0.8247 0.268 0.732
#> 24005     2  0.7674     0.8446 0.224 0.776
#> 24008     2  0.8386     0.8247 0.268 0.732
#> 24010     2  0.8327     0.8271 0.264 0.736
#> 24011     2  0.9323     0.7401 0.348 0.652
#> 24017     1  0.0000     0.8742 1.000 0.000
#> 24018     1  0.7139     0.6053 0.804 0.196
#> 24019     1  0.0000     0.8742 1.000 0.000
#> 24022     2  0.7528     0.8434 0.216 0.784
#> 25003     2  0.8443     0.8217 0.272 0.728
#> 25006     1  0.0000     0.8742 1.000 0.000
#> 26001     1  0.9775    -0.0934 0.588 0.412
#> 26003     2  0.7528     0.8434 0.216 0.784
#> 26005     2  0.9552     0.6961 0.376 0.624
#> 26008     1  0.0000     0.8742 1.000 0.000
#> 27003     2  0.7674     0.8446 0.224 0.776
#> 27004     2  0.7674     0.8446 0.224 0.776
#> 28001     2  0.7674     0.8446 0.224 0.776
#> 28003     2  0.7674     0.8446 0.224 0.776
#> 28005     2  0.7674     0.8446 0.224 0.776
#> 28006     2  0.7674     0.8446 0.224 0.776
#> 28007     2  0.7674     0.8446 0.224 0.776
#> 28019     1  0.0000     0.8742 1.000 0.000
#> 28021     1  0.0000     0.8742 1.000 0.000
#> 28023     2  0.7674     0.8446 0.224 0.776
#> 28024     2  0.7674     0.8446 0.224 0.776
#> 28028     2  0.7528     0.8434 0.216 0.784
#> 28031     2  0.8207     0.8316 0.256 0.744
#> 28032     2  0.7528     0.8434 0.216 0.784
#> 28035     1  0.0000     0.8742 1.000 0.000
#> 28036     2  0.7528     0.8434 0.216 0.784
#> 28037     1  0.0000     0.8742 1.000 0.000
#> 28042     2  0.7528     0.8434 0.216 0.784
#> 28043     2  0.7674     0.8446 0.224 0.776
#> 28044     2  0.7674     0.8446 0.224 0.776
#> 28047     2  0.7674     0.8446 0.224 0.776
#> 30001     1  0.0000     0.8742 1.000 0.000
#> 31007     2  0.7674     0.8446 0.224 0.776
#> 31011     2  0.7674     0.8446 0.224 0.776
#> 33005     1  0.0000     0.8742 1.000 0.000
#> 36001     1  0.0000     0.8742 1.000 0.000
#> 36002     2  0.8386     0.8247 0.268 0.732
#> 37013     2  0.9286     0.7457 0.344 0.656
#> 43001     1  0.9970    -0.3054 0.532 0.468
#> 43004     2  0.8713     0.8043 0.292 0.708
#> 43007     2  0.8207     0.8315 0.256 0.744
#> 43012     2  0.7674     0.8446 0.224 0.776
#> 48001     1  0.0000     0.8742 1.000 0.000
#> 49006     2  0.8443     0.8217 0.272 0.728
#> 57001     2  0.7674     0.8446 0.224 0.776
#> 62001     2  0.7674     0.8446 0.224 0.776
#> 62002     2  0.7674     0.8446 0.224 0.776
#> 62003     2  1.0000     0.4028 0.496 0.504
#> 63001     2  0.7950     0.8387 0.240 0.760
#> 64001     2  0.9286     0.7457 0.344 0.656
#> 64002     1  0.0000     0.8742 1.000 0.000
#> 65005     2  0.8386     0.8247 0.268 0.732
#> 68001     1  0.0000     0.8742 1.000 0.000
#> 68003     2  0.8386     0.8247 0.268 0.732
#> 84004     2  0.7674     0.8446 0.224 0.776
#> LAL5      2  0.7674     0.8446 0.224 0.776
#> 01003     2  0.0000     0.7512 0.000 1.000
#> 01007     2  0.0376     0.7489 0.004 0.996
#> 02020     2  0.0376     0.7489 0.004 0.996
#> 04018     2  0.0376     0.7489 0.004 0.996
#> 09002     2  0.0000     0.7512 0.000 1.000
#> 10005     2  0.0000     0.7512 0.000 1.000
#> 11002     2  0.0000     0.7512 0.000 1.000
#> 12008     2  0.0000     0.7512 0.000 1.000
#> 15006     1  0.7528     0.6473 0.784 0.216
#> 16002     2  0.0000     0.7512 0.000 1.000
#> 16007     2  0.0000     0.7512 0.000 1.000
#> 17003     2  0.7376     0.4904 0.208 0.792
#> 18001     2  0.0000     0.7512 0.000 1.000
#> 19002     2  0.0376     0.7489 0.004 0.996
#> 19008     2  0.0000     0.7512 0.000 1.000
#> 19014     2  0.0376     0.7489 0.004 0.996
#> 19017     2  0.0000     0.7512 0.000 1.000
#> 20005     2  0.0000     0.7512 0.000 1.000
#> 24006     2  0.0376     0.7489 0.004 0.996
#> 26009     1  0.7528     0.6473 0.784 0.216
#> 28008     2  0.0000     0.7512 0.000 1.000
#> 28009     2  0.0376     0.7489 0.004 0.996
#> 31015     2  0.0000     0.7512 0.000 1.000
#> 37001     2  0.0376     0.7489 0.004 0.996
#> 43006     2  0.0000     0.7512 0.000 1.000
#> 43015     2  0.0000     0.7512 0.000 1.000
#> 44001     2  0.0000     0.7512 0.000 1.000
#> 49004     2  0.0000     0.7512 0.000 1.000
#> 56007     2  0.0000     0.7512 0.000 1.000
#> 64005     2  0.0376     0.7489 0.004 0.996
#> 65003     2  0.0000     0.7512 0.000 1.000
#> 83001     2  0.0376     0.7489 0.004 0.996
#> LAL4      2  0.0376     0.7489 0.004 0.996

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-kmeans-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-CV-kmeans-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-CV-kmeans-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-CV-kmeans-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-kmeans-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-CV-kmeans-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-kmeans-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>             n sex(p) age(p)    BT(p) k
#> CV:kmeans 122  0.235  0.831 1.58e-01 2
#> CV:kmeans 125  0.338  0.494 2.25e-17 3
#> CV:kmeans 124  0.231  0.702 1.44e-19 4
#> CV:kmeans 114  0.299  0.623 8.94e-18 5
#> CV:kmeans  94  0.336  0.722 1.02e-13 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

CV:skmeans**

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk CV-skmeans-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk CV-skmeans-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.689           0.886       0.939         0.4941 0.497   0.497
#> 3 3 0.665           0.800       0.888         0.3293 0.766   0.566
#> 4 4 1.000           0.955       0.983         0.1469 0.844   0.583
#> 5 5 0.838           0.764       0.876         0.0571 0.955   0.819
#> 6 6 0.785           0.651       0.794         0.0355 0.973   0.873

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     1  0.0376      0.971 0.996 0.004
#> 01010     1  0.0000      0.972 1.000 0.000
#> 03002     1  0.1184      0.962 0.984 0.016
#> 04006     1  0.0000      0.972 1.000 0.000
#> 04007     1  0.9866      0.041 0.568 0.432
#> 04008     1  0.0000      0.972 1.000 0.000
#> 04010     1  0.0000      0.972 1.000 0.000
#> 04016     1  0.1184      0.962 0.984 0.016
#> 06002     1  0.0376      0.971 0.996 0.004
#> 08001     2  0.7219      0.814 0.200 0.800
#> 08011     1  0.0376      0.971 0.996 0.004
#> 08012     2  0.9775      0.466 0.412 0.588
#> 08018     1  0.2236      0.946 0.964 0.036
#> 08024     1  0.0376      0.971 0.996 0.004
#> 09008     1  0.0000      0.972 1.000 0.000
#> 09017     2  0.9491      0.572 0.368 0.632
#> 11005     2  0.7219      0.814 0.200 0.800
#> 12006     1  0.0376      0.971 0.996 0.004
#> 12007     1  0.0376      0.971 0.996 0.004
#> 12012     1  0.0376      0.971 0.996 0.004
#> 12019     1  0.0376      0.971 0.996 0.004
#> 12026     1  0.0000      0.972 1.000 0.000
#> 14016     1  0.0000      0.972 1.000 0.000
#> 15001     1  0.0376      0.971 0.996 0.004
#> 15004     2  0.0000      0.898 0.000 1.000
#> 15005     1  0.0000      0.972 1.000 0.000
#> 16004     1  0.0376      0.969 0.996 0.004
#> 16009     1  0.0000      0.972 1.000 0.000
#> 19005     1  0.0000      0.972 1.000 0.000
#> 20002     1  0.0000      0.972 1.000 0.000
#> 22009     1  0.0000      0.972 1.000 0.000
#> 22010     2  0.0376      0.897 0.004 0.996
#> 22011     1  0.1633      0.955 0.976 0.024
#> 22013     1  0.0000      0.972 1.000 0.000
#> 24001     1  0.1414      0.959 0.980 0.020
#> 24005     2  0.6531      0.834 0.168 0.832
#> 24008     1  0.2423      0.938 0.960 0.040
#> 24010     2  0.9963      0.326 0.464 0.536
#> 24011     1  0.0376      0.971 0.996 0.004
#> 24017     1  0.0000      0.972 1.000 0.000
#> 24018     1  0.0000      0.972 1.000 0.000
#> 24019     1  0.0000      0.972 1.000 0.000
#> 24022     2  0.5294      0.857 0.120 0.880
#> 25003     1  0.0376      0.971 0.996 0.004
#> 25006     1  0.0000      0.972 1.000 0.000
#> 26001     1  0.0000      0.972 1.000 0.000
#> 26003     2  0.7219      0.814 0.200 0.800
#> 26005     1  0.0376      0.971 0.996 0.004
#> 26008     1  0.0000      0.972 1.000 0.000
#> 27003     2  0.7139      0.819 0.196 0.804
#> 27004     2  0.7219      0.814 0.200 0.800
#> 28001     2  0.7528      0.804 0.216 0.784
#> 28003     2  0.0376      0.897 0.004 0.996
#> 28005     2  0.7219      0.814 0.200 0.800
#> 28006     2  0.7139      0.817 0.196 0.804
#> 28007     2  0.7219      0.814 0.200 0.800
#> 28019     1  0.0000      0.972 1.000 0.000
#> 28021     1  0.0000      0.972 1.000 0.000
#> 28023     2  0.7056      0.820 0.192 0.808
#> 28024     2  0.7219      0.814 0.200 0.800
#> 28028     2  0.0000      0.898 0.000 1.000
#> 28031     2  0.8499      0.731 0.276 0.724
#> 28032     2  0.0000      0.898 0.000 1.000
#> 28035     1  0.0000      0.972 1.000 0.000
#> 28036     2  0.4431      0.868 0.092 0.908
#> 28037     1  0.0000      0.972 1.000 0.000
#> 28042     2  0.0000      0.898 0.000 1.000
#> 28043     2  0.7219      0.814 0.200 0.800
#> 28044     2  0.7299      0.813 0.204 0.796
#> 28047     2  0.5946      0.846 0.144 0.856
#> 30001     1  0.0000      0.972 1.000 0.000
#> 31007     2  0.0000      0.898 0.000 1.000
#> 31011     2  0.7219      0.814 0.200 0.800
#> 33005     1  0.0000      0.972 1.000 0.000
#> 36001     1  0.0000      0.972 1.000 0.000
#> 36002     1  0.1843      0.951 0.972 0.028
#> 37013     1  0.0000      0.972 1.000 0.000
#> 43001     1  0.0000      0.972 1.000 0.000
#> 43004     1  0.0000      0.972 1.000 0.000
#> 43007     2  0.9686      0.505 0.396 0.604
#> 43012     2  0.0000      0.898 0.000 1.000
#> 48001     1  0.0000      0.972 1.000 0.000
#> 49006     1  0.0376      0.971 0.996 0.004
#> 57001     2  0.0000      0.898 0.000 1.000
#> 62001     2  0.7299      0.813 0.204 0.796
#> 62002     2  0.7528      0.803 0.216 0.784
#> 62003     1  0.0000      0.972 1.000 0.000
#> 63001     2  0.9686      0.505 0.396 0.604
#> 64001     1  0.0376      0.971 0.996 0.004
#> 64002     1  0.0000      0.972 1.000 0.000
#> 65005     1  0.0376      0.971 0.996 0.004
#> 68001     1  0.0000      0.972 1.000 0.000
#> 68003     1  0.1843      0.951 0.972 0.028
#> 84004     2  0.7219      0.814 0.200 0.800
#> LAL5      2  0.0000      0.898 0.000 1.000
#> 01003     2  0.0000      0.898 0.000 1.000
#> 01007     2  0.0376      0.897 0.004 0.996
#> 02020     2  0.0376      0.897 0.004 0.996
#> 04018     2  0.0376      0.897 0.004 0.996
#> 09002     2  0.0000      0.898 0.000 1.000
#> 10005     2  0.0000      0.898 0.000 1.000
#> 11002     2  0.0000      0.898 0.000 1.000
#> 12008     2  0.0000      0.898 0.000 1.000
#> 15006     1  0.7219      0.731 0.800 0.200
#> 16002     2  0.0000      0.898 0.000 1.000
#> 16007     2  0.0000      0.898 0.000 1.000
#> 17003     1  0.9686      0.368 0.604 0.396
#> 18001     2  0.0000      0.898 0.000 1.000
#> 19002     2  0.0376      0.897 0.004 0.996
#> 19008     2  0.0000      0.898 0.000 1.000
#> 19014     2  0.0376      0.897 0.004 0.996
#> 19017     2  0.0000      0.898 0.000 1.000
#> 20005     2  0.0000      0.898 0.000 1.000
#> 24006     2  0.0376      0.897 0.004 0.996
#> 26009     1  0.7219      0.731 0.800 0.200
#> 28008     2  0.0000      0.898 0.000 1.000
#> 28009     2  0.0376      0.897 0.004 0.996
#> 31015     2  0.0000      0.898 0.000 1.000
#> 37001     2  0.0376      0.897 0.004 0.996
#> 43006     2  0.0000      0.898 0.000 1.000
#> 43015     2  0.0000      0.898 0.000 1.000
#> 44001     2  0.0000      0.898 0.000 1.000
#> 49004     2  0.0000      0.898 0.000 1.000
#> 56007     2  0.0000      0.898 0.000 1.000
#> 64005     2  0.0376      0.897 0.004 0.996
#> 65003     2  0.0376      0.897 0.004 0.996
#> 83001     2  0.0376      0.897 0.004 0.996
#> LAL4      2  0.0376      0.897 0.004 0.996

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-skmeans-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-CV-skmeans-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-CV-skmeans-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-CV-skmeans-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-skmeans-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-CV-skmeans-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-skmeans-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>              n sex(p) age(p)    BT(p) k
#> CV:skmeans 124  0.608  0.906 2.83e-07 2
#> CV:skmeans 122  0.278  0.864 9.33e-08 3
#> CV:skmeans 124  0.283  0.678 8.91e-20 4
#> CV:skmeans 116  0.294  0.752 1.01e-14 5
#> CV:skmeans 100  0.346  0.896 2.52e-13 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

CV:pam

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk CV-pam-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk CV-pam-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.452           0.582       0.746         0.4573 0.497   0.497
#> 3 3 0.458           0.688       0.786         0.4003 0.590   0.358
#> 4 4 0.893           0.882       0.952         0.1639 0.839   0.592
#> 5 5 0.846           0.782       0.906         0.0576 0.931   0.745
#> 6 6 0.797           0.702       0.862         0.0339 0.968   0.852

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     1  1.0000     0.6778 0.500 0.500
#> 01010     1  0.9896     0.7577 0.560 0.440
#> 03002     2  0.1843     0.6618 0.028 0.972
#> 04006     1  0.9896     0.7577 0.560 0.440
#> 04007     2  0.1843     0.6618 0.028 0.972
#> 04008     1  0.9896     0.7577 0.560 0.440
#> 04010     1  0.9896     0.7577 0.560 0.440
#> 04016     2  0.6247     0.4333 0.156 0.844
#> 06002     1  0.9896     0.7577 0.560 0.440
#> 08001     2  0.0000     0.6912 0.000 1.000
#> 08011     1  1.0000     0.6778 0.500 0.500
#> 08012     2  1.0000    -0.6878 0.500 0.500
#> 08018     1  0.9970     0.6559 0.532 0.468
#> 08024     1  0.9896     0.7577 0.560 0.440
#> 09008     1  0.9896     0.7577 0.560 0.440
#> 09017     2  0.6531     0.3574 0.168 0.832
#> 11005     2  0.0000     0.6912 0.000 1.000
#> 12006     1  1.0000     0.6778 0.500 0.500
#> 12007     2  1.0000    -0.6878 0.500 0.500
#> 12012     2  1.0000    -0.6878 0.500 0.500
#> 12019     1  0.9896     0.7577 0.560 0.440
#> 12026     1  0.9896     0.7577 0.560 0.440
#> 14016     1  0.9896     0.7577 0.560 0.440
#> 15001     1  0.9896     0.7577 0.560 0.440
#> 15004     2  0.0000     0.6912 0.000 1.000
#> 15005     1  0.9896     0.7577 0.560 0.440
#> 16004     1  0.9881     0.7559 0.564 0.436
#> 16009     1  0.9881     0.7560 0.564 0.436
#> 19005     1  0.9896     0.7577 0.560 0.440
#> 20002     1  0.9896     0.7577 0.560 0.440
#> 22009     1  0.9896     0.7577 0.560 0.440
#> 22010     1  0.9000     0.3235 0.684 0.316
#> 22011     1  1.0000     0.6778 0.500 0.500
#> 22013     1  0.9896     0.7577 0.560 0.440
#> 24001     2  0.5519     0.4809 0.128 0.872
#> 24005     2  0.0000     0.6912 0.000 1.000
#> 24008     1  0.9922     0.7490 0.552 0.448
#> 24010     2  0.0000     0.6912 0.000 1.000
#> 24011     1  0.9896     0.7577 0.560 0.440
#> 24017     1  0.9896     0.7577 0.560 0.440
#> 24018     1  0.9896     0.7577 0.560 0.440
#> 24019     1  0.9881     0.7560 0.564 0.436
#> 24022     2  0.0000     0.6912 0.000 1.000
#> 25003     1  0.9909     0.7535 0.556 0.444
#> 25006     1  0.9896     0.7577 0.560 0.440
#> 26001     1  0.9896     0.7577 0.560 0.440
#> 26003     2  0.0000     0.6912 0.000 1.000
#> 26005     1  0.9896     0.7577 0.560 0.440
#> 26008     1  0.9896     0.7577 0.560 0.440
#> 27003     2  0.0000     0.6912 0.000 1.000
#> 27004     2  0.0000     0.6912 0.000 1.000
#> 28001     1  0.9393     0.6489 0.644 0.356
#> 28003     1  0.9970    -0.3909 0.532 0.468
#> 28005     2  0.0000     0.6912 0.000 1.000
#> 28006     2  0.0000     0.6912 0.000 1.000
#> 28007     2  0.0000     0.6912 0.000 1.000
#> 28019     1  0.9896     0.7577 0.560 0.440
#> 28021     1  0.9896     0.7577 0.560 0.440
#> 28023     2  0.0000     0.6912 0.000 1.000
#> 28024     2  0.0000     0.6912 0.000 1.000
#> 28028     2  0.0000     0.6912 0.000 1.000
#> 28031     1  0.9970     0.7263 0.532 0.468
#> 28032     2  0.0000     0.6912 0.000 1.000
#> 28035     1  0.9896     0.7577 0.560 0.440
#> 28036     2  0.0000     0.6912 0.000 1.000
#> 28037     1  0.9896     0.7577 0.560 0.440
#> 28042     2  0.4431     0.6420 0.092 0.908
#> 28043     2  0.0000     0.6912 0.000 1.000
#> 28044     2  0.0000     0.6912 0.000 1.000
#> 28047     2  0.0000     0.6912 0.000 1.000
#> 30001     1  0.9896     0.7577 0.560 0.440
#> 31007     2  0.8499    -0.0124 0.276 0.724
#> 31011     2  0.0000     0.6912 0.000 1.000
#> 33005     1  0.9896     0.7577 0.560 0.440
#> 36001     1  0.9608     0.7174 0.616 0.384
#> 36002     2  0.1843     0.6618 0.028 0.972
#> 37013     1  1.0000     0.6840 0.504 0.496
#> 43001     1  0.9896     0.7577 0.560 0.440
#> 43004     2  0.8386     0.0453 0.268 0.732
#> 43007     2  0.0672     0.6838 0.008 0.992
#> 43012     2  0.0672     0.6885 0.008 0.992
#> 48001     1  0.9896     0.7577 0.560 0.440
#> 49006     2  0.1843     0.6618 0.028 0.972
#> 57001     2  0.3274     0.6300 0.060 0.940
#> 62001     2  0.0000     0.6912 0.000 1.000
#> 62002     2  0.0000     0.6912 0.000 1.000
#> 62003     1  0.9896     0.7577 0.560 0.440
#> 63001     2  0.0000     0.6912 0.000 1.000
#> 64001     1  1.0000     0.6778 0.500 0.500
#> 64002     1  0.9896     0.7577 0.560 0.440
#> 65005     2  0.1633     0.6666 0.024 0.976
#> 68001     1  0.9881     0.7560 0.564 0.436
#> 68003     2  0.0672     0.6839 0.008 0.992
#> 84004     2  0.0000     0.6912 0.000 1.000
#> LAL5      2  0.1843     0.6788 0.028 0.972
#> 01003     2  0.9896     0.4872 0.440 0.560
#> 01007     1  0.0000     0.4291 1.000 0.000
#> 02020     1  0.0000     0.4291 1.000 0.000
#> 04018     2  0.9922     0.4814 0.448 0.552
#> 09002     2  0.9933     0.4800 0.452 0.548
#> 10005     2  0.9866     0.4894 0.432 0.568
#> 11002     2  0.9896     0.4872 0.440 0.560
#> 12008     1  0.1414     0.4121 0.980 0.020
#> 15006     1  0.0000     0.4291 1.000 0.000
#> 16002     2  0.9896     0.4872 0.440 0.560
#> 16007     2  0.9896     0.4872 0.440 0.560
#> 17003     1  0.0000     0.4291 1.000 0.000
#> 18001     2  0.9896     0.4872 0.440 0.560
#> 19002     1  0.0000     0.4291 1.000 0.000
#> 19008     2  0.9896     0.4872 0.440 0.560
#> 19014     1  0.0000     0.4291 1.000 0.000
#> 19017     2  0.9896     0.4872 0.440 0.560
#> 20005     2  0.9896     0.4872 0.440 0.560
#> 24006     1  0.0000     0.4291 1.000 0.000
#> 26009     1  0.0000     0.4291 1.000 0.000
#> 28008     2  0.9896     0.4872 0.440 0.560
#> 28009     1  0.1843     0.4008 0.972 0.028
#> 31015     2  0.9896     0.4872 0.440 0.560
#> 37001     1  0.0000     0.4291 1.000 0.000
#> 43006     2  0.9896     0.4872 0.440 0.560
#> 43015     1  0.8955    -0.1634 0.688 0.312
#> 44001     1  0.3879     0.3495 0.924 0.076
#> 49004     2  0.9896     0.4872 0.440 0.560
#> 56007     2  0.9896     0.4872 0.440 0.560
#> 64005     1  0.0000     0.4291 1.000 0.000
#> 65003     2  0.9896     0.4872 0.440 0.560
#> 83001     1  0.0000     0.4291 1.000 0.000
#> LAL4      1  0.1843     0.4008 0.972 0.028

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-pam-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-CV-pam-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-CV-pam-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-CV-pam-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-pam-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-CV-pam-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-pam-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>          n sex(p) age(p)    BT(p) k
#> CV:pam  85  0.553  0.121 1.49e-01 2
#> CV:pam 113  0.278  0.874 9.29e-05 3
#> CV:pam 122  0.557  0.807 4.47e-15 4
#> CV:pam 112  0.633  0.856 1.19e-14 5
#> CV:pam 103  0.509  0.765 1.38e-22 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

CV:mclust*

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'mclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk CV-mclust-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk CV-mclust-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.983       0.992         0.3902 0.614   0.614
#> 3 3 0.577           0.705       0.821         0.6195 0.725   0.552
#> 4 4 0.942           0.936       0.971         0.1794 0.910   0.737
#> 5 5 0.831           0.858       0.871         0.0399 1.000   1.000
#> 6 6 0.792           0.658       0.795         0.0332 0.924   0.713

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4
#> attr(,"optional")
#> [1] 2

There is also optional best \(k\) = 2 that is worth to check.

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     1  0.0000      0.991 1.000 0.000
#> 01010     1  0.0376      0.990 0.996 0.004
#> 03002     1  0.0000      0.991 1.000 0.000
#> 04006     1  0.0376      0.990 0.996 0.004
#> 04007     1  0.0000      0.991 1.000 0.000
#> 04008     1  0.0376      0.990 0.996 0.004
#> 04010     1  0.0376      0.990 0.996 0.004
#> 04016     1  0.0000      0.991 1.000 0.000
#> 06002     1  0.0000      0.991 1.000 0.000
#> 08001     1  0.0000      0.991 1.000 0.000
#> 08011     1  0.0000      0.991 1.000 0.000
#> 08012     1  0.0000      0.991 1.000 0.000
#> 08018     1  0.0000      0.991 1.000 0.000
#> 08024     1  0.0000      0.991 1.000 0.000
#> 09008     1  0.0376      0.990 0.996 0.004
#> 09017     1  0.0000      0.991 1.000 0.000
#> 11005     1  0.0000      0.991 1.000 0.000
#> 12006     1  0.0000      0.991 1.000 0.000
#> 12007     1  0.0000      0.991 1.000 0.000
#> 12012     1  0.0000      0.991 1.000 0.000
#> 12019     1  0.0000      0.991 1.000 0.000
#> 12026     1  0.0376      0.990 0.996 0.004
#> 14016     1  0.0376      0.990 0.996 0.004
#> 15001     1  0.0000      0.991 1.000 0.000
#> 15004     1  0.0000      0.991 1.000 0.000
#> 15005     1  0.0376      0.990 0.996 0.004
#> 16004     1  0.0672      0.987 0.992 0.008
#> 16009     1  0.0376      0.990 0.996 0.004
#> 19005     1  0.0376      0.990 0.996 0.004
#> 20002     1  0.0376      0.990 0.996 0.004
#> 22009     1  0.0000      0.991 1.000 0.000
#> 22010     1  0.8608      0.615 0.716 0.284
#> 22011     1  0.0000      0.991 1.000 0.000
#> 22013     1  0.0000      0.991 1.000 0.000
#> 24001     1  0.0000      0.991 1.000 0.000
#> 24005     1  0.0000      0.991 1.000 0.000
#> 24008     1  0.0000      0.991 1.000 0.000
#> 24010     1  0.0376      0.990 0.996 0.004
#> 24011     1  0.0000      0.991 1.000 0.000
#> 24017     1  0.0376      0.990 0.996 0.004
#> 24018     1  0.0376      0.990 0.996 0.004
#> 24019     1  0.0376      0.990 0.996 0.004
#> 24022     1  0.0000      0.991 1.000 0.000
#> 25003     1  0.0000      0.991 1.000 0.000
#> 25006     1  0.0376      0.990 0.996 0.004
#> 26001     1  0.0000      0.991 1.000 0.000
#> 26003     1  0.0000      0.991 1.000 0.000
#> 26005     1  0.0000      0.991 1.000 0.000
#> 26008     1  0.0376      0.990 0.996 0.004
#> 27003     1  0.0376      0.990 0.996 0.004
#> 27004     1  0.0000      0.991 1.000 0.000
#> 28001     1  0.7219      0.758 0.800 0.200
#> 28003     1  0.0376      0.990 0.996 0.004
#> 28005     1  0.0000      0.991 1.000 0.000
#> 28006     1  0.0376      0.990 0.996 0.004
#> 28007     1  0.0000      0.991 1.000 0.000
#> 28019     1  0.0376      0.990 0.996 0.004
#> 28021     1  0.0376      0.990 0.996 0.004
#> 28023     1  0.0000      0.991 1.000 0.000
#> 28024     1  0.0000      0.991 1.000 0.000
#> 28028     1  0.0000      0.991 1.000 0.000
#> 28031     1  0.0000      0.991 1.000 0.000
#> 28032     1  0.0000      0.991 1.000 0.000
#> 28035     1  0.0376      0.990 0.996 0.004
#> 28036     1  0.0000      0.991 1.000 0.000
#> 28037     1  0.0376      0.990 0.996 0.004
#> 28042     1  0.0376      0.990 0.996 0.004
#> 28043     1  0.0000      0.991 1.000 0.000
#> 28044     1  0.0000      0.991 1.000 0.000
#> 28047     1  0.0000      0.991 1.000 0.000
#> 30001     1  0.0376      0.990 0.996 0.004
#> 31007     1  0.7219      0.758 0.800 0.200
#> 31011     1  0.0000      0.991 1.000 0.000
#> 33005     1  0.0376      0.990 0.996 0.004
#> 36001     1  0.0376      0.990 0.996 0.004
#> 36002     1  0.0000      0.991 1.000 0.000
#> 37013     1  0.0000      0.991 1.000 0.000
#> 43001     1  0.0000      0.991 1.000 0.000
#> 43004     1  0.0000      0.991 1.000 0.000
#> 43007     1  0.0000      0.991 1.000 0.000
#> 43012     1  0.0000      0.991 1.000 0.000
#> 48001     1  0.0376      0.990 0.996 0.004
#> 49006     1  0.0000      0.991 1.000 0.000
#> 57001     1  0.0000      0.991 1.000 0.000
#> 62001     1  0.0000      0.991 1.000 0.000
#> 62002     1  0.0000      0.991 1.000 0.000
#> 62003     1  0.0376      0.990 0.996 0.004
#> 63001     1  0.0376      0.990 0.996 0.004
#> 64001     1  0.0000      0.991 1.000 0.000
#> 64002     1  0.0376      0.990 0.996 0.004
#> 65005     1  0.0000      0.991 1.000 0.000
#> 68001     1  0.0376      0.990 0.996 0.004
#> 68003     1  0.0000      0.991 1.000 0.000
#> 84004     1  0.0000      0.991 1.000 0.000
#> LAL5      1  0.0000      0.991 1.000 0.000
#> 01003     2  0.0000      0.994 0.000 1.000
#> 01007     2  0.0000      0.994 0.000 1.000
#> 02020     2  0.0000      0.994 0.000 1.000
#> 04018     2  0.0000      0.994 0.000 1.000
#> 09002     2  0.0000      0.994 0.000 1.000
#> 10005     2  0.0000      0.994 0.000 1.000
#> 11002     2  0.0000      0.994 0.000 1.000
#> 12008     2  0.0000      0.994 0.000 1.000
#> 15006     2  0.5737      0.843 0.136 0.864
#> 16002     2  0.0000      0.994 0.000 1.000
#> 16007     2  0.0000      0.994 0.000 1.000
#> 17003     2  0.0000      0.994 0.000 1.000
#> 18001     2  0.0000      0.994 0.000 1.000
#> 19002     2  0.0000      0.994 0.000 1.000
#> 19008     2  0.0000      0.994 0.000 1.000
#> 19014     2  0.0000      0.994 0.000 1.000
#> 19017     2  0.0000      0.994 0.000 1.000
#> 20005     2  0.0000      0.994 0.000 1.000
#> 24006     2  0.0000      0.994 0.000 1.000
#> 26009     2  0.3114      0.939 0.056 0.944
#> 28008     2  0.0000      0.994 0.000 1.000
#> 28009     2  0.0000      0.994 0.000 1.000
#> 31015     2  0.0000      0.994 0.000 1.000
#> 37001     2  0.0000      0.994 0.000 1.000
#> 43006     2  0.0000      0.994 0.000 1.000
#> 43015     2  0.0000      0.994 0.000 1.000
#> 44001     2  0.0000      0.994 0.000 1.000
#> 49004     2  0.0000      0.994 0.000 1.000
#> 56007     2  0.0000      0.994 0.000 1.000
#> 64005     2  0.0000      0.994 0.000 1.000
#> 65003     2  0.0000      0.994 0.000 1.000
#> 83001     2  0.0000      0.994 0.000 1.000
#> LAL4      2  0.0000      0.994 0.000 1.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-mclust-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-CV-mclust-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-CV-mclust-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-CV-mclust-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-mclust-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-CV-mclust-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-mclust-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>             n sex(p) age(p)    BT(p) k
#> CV:mclust 128  0.329  0.173 3.06e-23 2
#> CV:mclust 108  0.143  0.342 1.42e-21 3
#> CV:mclust 127  0.172  0.596 8.78e-22 4
#> CV:mclust 128  0.157  0.523 1.21e-21 5
#> CV:mclust  96  0.364  0.784 1.94e-12 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

CV:NMF*

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'NMF' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk CV-NMF-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk CV-NMF-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.422           0.746       0.873         0.4490 0.532   0.532
#> 3 3 0.698           0.801       0.907         0.4293 0.692   0.482
#> 4 4 0.942           0.939       0.973         0.1682 0.830   0.558
#> 5 5 0.776           0.719       0.857         0.0636 0.917   0.687
#> 6 6 0.789           0.701       0.851         0.0363 0.927   0.672

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     1  0.9710     0.1568 0.600 0.400
#> 01010     1  0.0000     0.8797 1.000 0.000
#> 03002     2  0.9686     0.5490 0.396 0.604
#> 04006     1  0.0000     0.8797 1.000 0.000
#> 04007     2  0.9710     0.5412 0.400 0.600
#> 04008     1  0.0000     0.8797 1.000 0.000
#> 04010     1  0.0000     0.8797 1.000 0.000
#> 04016     2  0.9754     0.5238 0.408 0.592
#> 06002     1  0.2948     0.8413 0.948 0.052
#> 08001     2  0.8443     0.7319 0.272 0.728
#> 08011     1  0.9795     0.0931 0.584 0.416
#> 08012     2  0.7299     0.7909 0.204 0.796
#> 08018     2  0.7815     0.7703 0.232 0.768
#> 08024     1  0.6438     0.7126 0.836 0.164
#> 09008     1  0.0000     0.8797 1.000 0.000
#> 09017     2  0.8661     0.7137 0.288 0.712
#> 11005     2  0.7453     0.7857 0.212 0.788
#> 12006     2  0.9896     0.4426 0.440 0.560
#> 12007     1  0.9933    -0.0723 0.548 0.452
#> 12012     1  0.9815     0.0760 0.580 0.420
#> 12019     1  0.9460     0.2825 0.636 0.364
#> 12026     1  0.0000     0.8797 1.000 0.000
#> 14016     1  0.0000     0.8797 1.000 0.000
#> 15001     1  0.0000     0.8797 1.000 0.000
#> 15004     2  0.7219     0.7932 0.200 0.800
#> 15005     1  0.0000     0.8797 1.000 0.000
#> 16004     1  0.0000     0.8797 1.000 0.000
#> 16009     1  0.0000     0.8797 1.000 0.000
#> 19005     1  0.0000     0.8797 1.000 0.000
#> 20002     1  0.0000     0.8797 1.000 0.000
#> 22009     2  0.9833     0.4855 0.424 0.576
#> 22010     2  0.0000     0.8143 0.000 1.000
#> 22011     2  0.9710     0.5412 0.400 0.600
#> 22013     1  0.0938     0.8722 0.988 0.012
#> 24001     2  0.9833     0.4854 0.424 0.576
#> 24005     2  0.7219     0.7932 0.200 0.800
#> 24008     2  0.9732     0.5327 0.404 0.596
#> 24010     2  0.9635     0.5640 0.388 0.612
#> 24011     1  0.9393     0.3073 0.644 0.356
#> 24017     1  0.0000     0.8797 1.000 0.000
#> 24018     1  0.0000     0.8797 1.000 0.000
#> 24019     1  0.0000     0.8797 1.000 0.000
#> 24022     2  0.4690     0.8138 0.100 0.900
#> 25003     2  0.9710     0.5412 0.400 0.600
#> 25006     1  0.0000     0.8797 1.000 0.000
#> 26001     1  0.0000     0.8797 1.000 0.000
#> 26003     2  0.7219     0.7932 0.200 0.800
#> 26005     1  0.3879     0.8189 0.924 0.076
#> 26008     1  0.0000     0.8797 1.000 0.000
#> 27003     2  0.7219     0.7932 0.200 0.800
#> 27004     2  0.7219     0.7932 0.200 0.800
#> 28001     2  0.7219     0.7932 0.200 0.800
#> 28003     2  0.5737     0.8086 0.136 0.864
#> 28005     2  0.7219     0.7932 0.200 0.800
#> 28006     2  0.7219     0.7932 0.200 0.800
#> 28007     2  0.7219     0.7932 0.200 0.800
#> 28019     1  0.0000     0.8797 1.000 0.000
#> 28021     1  0.0000     0.8797 1.000 0.000
#> 28023     2  0.7219     0.7932 0.200 0.800
#> 28024     2  0.7219     0.7932 0.200 0.800
#> 28028     2  0.1184     0.8148 0.016 0.984
#> 28031     2  0.9209     0.6507 0.336 0.664
#> 28032     2  0.0000     0.8143 0.000 1.000
#> 28035     1  0.0000     0.8797 1.000 0.000
#> 28036     2  0.3431     0.8151 0.064 0.936
#> 28037     1  0.0000     0.8797 1.000 0.000
#> 28042     2  0.0000     0.8143 0.000 1.000
#> 28043     2  0.7219     0.7932 0.200 0.800
#> 28044     2  0.8327     0.7404 0.264 0.736
#> 28047     2  0.7219     0.7932 0.200 0.800
#> 30001     1  0.0000     0.8797 1.000 0.000
#> 31007     2  0.5178     0.8121 0.116 0.884
#> 31011     2  0.7674     0.7770 0.224 0.776
#> 33005     1  0.0000     0.8797 1.000 0.000
#> 36001     1  0.0000     0.8797 1.000 0.000
#> 36002     2  0.9710     0.5412 0.400 0.600
#> 37013     1  0.3431     0.8308 0.936 0.064
#> 43001     1  0.0672     0.8748 0.992 0.008
#> 43004     1  0.7056     0.6707 0.808 0.192
#> 43007     2  0.8081     0.7562 0.248 0.752
#> 43012     2  0.4690     0.8140 0.100 0.900
#> 48001     1  0.0000     0.8797 1.000 0.000
#> 49006     1  0.9896    -0.0162 0.560 0.440
#> 57001     2  0.6973     0.7968 0.188 0.812
#> 62001     2  0.9209     0.6507 0.336 0.664
#> 62002     2  0.9209     0.6521 0.336 0.664
#> 62003     1  0.0000     0.8797 1.000 0.000
#> 63001     2  0.7299     0.7909 0.204 0.796
#> 64001     1  0.8909     0.4381 0.692 0.308
#> 64002     1  0.0000     0.8797 1.000 0.000
#> 65005     2  0.9775     0.5147 0.412 0.588
#> 68001     1  0.0000     0.8797 1.000 0.000
#> 68003     2  0.9710     0.5412 0.400 0.600
#> 84004     2  0.7674     0.7770 0.224 0.776
#> LAL5      2  0.4562     0.8142 0.096 0.904
#> 01003     2  0.0000     0.8143 0.000 1.000
#> 01007     2  0.0000     0.8143 0.000 1.000
#> 02020     2  0.0000     0.8143 0.000 1.000
#> 04018     2  0.0000     0.8143 0.000 1.000
#> 09002     2  0.0000     0.8143 0.000 1.000
#> 10005     2  0.0000     0.8143 0.000 1.000
#> 11002     2  0.0000     0.8143 0.000 1.000
#> 12008     2  0.0000     0.8143 0.000 1.000
#> 15006     1  0.7299     0.6564 0.796 0.204
#> 16002     2  0.0000     0.8143 0.000 1.000
#> 16007     2  0.0000     0.8143 0.000 1.000
#> 17003     2  0.0376     0.8121 0.004 0.996
#> 18001     2  0.0000     0.8143 0.000 1.000
#> 19002     2  0.0000     0.8143 0.000 1.000
#> 19008     2  0.0000     0.8143 0.000 1.000
#> 19014     2  0.0000     0.8143 0.000 1.000
#> 19017     2  0.0000     0.8143 0.000 1.000
#> 20005     2  0.0000     0.8143 0.000 1.000
#> 24006     2  0.0000     0.8143 0.000 1.000
#> 26009     1  0.7299     0.6564 0.796 0.204
#> 28008     2  0.0000     0.8143 0.000 1.000
#> 28009     2  0.0000     0.8143 0.000 1.000
#> 31015     2  0.0000     0.8143 0.000 1.000
#> 37001     2  0.0000     0.8143 0.000 1.000
#> 43006     2  0.0000     0.8143 0.000 1.000
#> 43015     2  0.0000     0.8143 0.000 1.000
#> 44001     2  0.0000     0.8143 0.000 1.000
#> 49004     2  0.0000     0.8143 0.000 1.000
#> 56007     2  0.0000     0.8143 0.000 1.000
#> 64005     2  0.0000     0.8143 0.000 1.000
#> 65003     2  0.0000     0.8143 0.000 1.000
#> 83001     2  0.0000     0.8143 0.000 1.000
#> LAL4      2  0.0000     0.8143 0.000 1.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-NMF-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-CV-NMF-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-CV-NMF-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-CV-NMF-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-NMF-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-CV-NMF-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-NMF-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>          n sex(p) age(p)    BT(p) k
#> CV:NMF 117  0.944  0.666 2.63e-03 2
#> CV:NMF 117  0.182  0.701 3.30e-08 3
#> CV:NMF 126  0.296  0.609 4.09e-19 4
#> CV:NMF 109  0.319  0.759 5.65e-13 5
#> CV:NMF 106  0.603  0.509 9.06e-14 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

MAD:hclust

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'hclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk MAD-hclust-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk MAD-hclust-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.460           0.864       0.919         0.3605 0.674   0.674
#> 3 3 0.328           0.663       0.785         0.6718 0.688   0.537
#> 4 4 0.470           0.500       0.704         0.1966 0.853   0.623
#> 5 5 0.544           0.565       0.703         0.0793 0.908   0.690
#> 6 6 0.597           0.480       0.632         0.0482 0.914   0.651

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 3

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2  0.2043     0.9146 0.032 0.968
#> 01010     1  0.0376     0.9054 0.996 0.004
#> 03002     2  0.2236     0.9146 0.036 0.964
#> 04006     1  0.0376     0.9054 0.996 0.004
#> 04007     2  0.0000     0.9155 0.000 1.000
#> 04008     1  0.9983     0.0301 0.524 0.476
#> 04010     1  0.0376     0.9054 0.996 0.004
#> 04016     2  0.0000     0.9155 0.000 1.000
#> 06002     2  0.4815     0.8869 0.104 0.896
#> 08001     2  0.0000     0.9155 0.000 1.000
#> 08011     2  0.2043     0.9146 0.032 0.968
#> 08012     2  0.0938     0.9169 0.012 0.988
#> 08018     2  0.3431     0.9056 0.064 0.936
#> 08024     2  0.3274     0.9083 0.060 0.940
#> 09008     1  0.6247     0.8218 0.844 0.156
#> 09017     2  0.5737     0.8668 0.136 0.864
#> 11005     2  0.0000     0.9155 0.000 1.000
#> 12006     2  0.6148     0.8609 0.152 0.848
#> 12007     2  0.2043     0.9146 0.032 0.968
#> 12012     2  0.5737     0.8680 0.136 0.864
#> 12019     2  0.2423     0.9130 0.040 0.960
#> 12026     2  0.6623     0.8385 0.172 0.828
#> 14016     2  0.6623     0.8385 0.172 0.828
#> 15001     2  0.3114     0.9093 0.056 0.944
#> 15004     2  0.6887     0.8276 0.184 0.816
#> 15005     1  0.6247     0.8218 0.844 0.156
#> 16004     1  0.5737     0.8283 0.864 0.136
#> 16009     1  0.0376     0.9054 0.996 0.004
#> 19005     1  0.5737     0.8283 0.864 0.136
#> 20002     1  0.9833     0.2308 0.576 0.424
#> 22009     2  0.6531     0.8445 0.168 0.832
#> 22010     2  0.6887     0.8339 0.184 0.816
#> 22011     2  0.0672     0.9165 0.008 0.992
#> 22013     2  0.6887     0.8247 0.184 0.816
#> 24001     2  0.0376     0.9161 0.004 0.996
#> 24005     2  0.1843     0.9169 0.028 0.972
#> 24008     2  0.3114     0.9093 0.056 0.944
#> 24010     2  0.6148     0.8609 0.152 0.848
#> 24011     2  0.4161     0.8977 0.084 0.916
#> 24017     1  0.5737     0.8413 0.864 0.136
#> 24018     2  0.9983     0.1919 0.476 0.524
#> 24019     1  0.0376     0.9054 0.996 0.004
#> 24022     2  0.0000     0.9155 0.000 1.000
#> 25003     2  0.2236     0.9131 0.036 0.964
#> 25006     1  0.0376     0.9054 0.996 0.004
#> 26001     2  0.4815     0.8869 0.104 0.896
#> 26003     2  0.0000     0.9155 0.000 1.000
#> 26005     2  0.3274     0.9064 0.060 0.940
#> 26008     1  0.0376     0.9054 0.996 0.004
#> 27003     2  0.8861     0.6606 0.304 0.696
#> 27004     2  0.0376     0.9163 0.004 0.996
#> 28001     2  0.9129     0.6196 0.328 0.672
#> 28003     2  0.4161     0.9009 0.084 0.916
#> 28005     2  0.0376     0.9163 0.004 0.996
#> 28006     2  0.6148     0.8579 0.152 0.848
#> 28007     2  0.0376     0.9163 0.004 0.996
#> 28019     1  0.3584     0.8991 0.932 0.068
#> 28021     1  0.3584     0.8991 0.932 0.068
#> 28023     2  0.1184     0.9160 0.016 0.984
#> 28024     2  0.0376     0.9163 0.004 0.996
#> 28028     2  0.0000     0.9155 0.000 1.000
#> 28031     2  0.2043     0.9158 0.032 0.968
#> 28032     2  0.0000     0.9155 0.000 1.000
#> 28035     1  0.3584     0.8991 0.932 0.068
#> 28036     2  0.0000     0.9155 0.000 1.000
#> 28037     1  0.3584     0.8991 0.932 0.068
#> 28042     2  0.5178     0.8828 0.116 0.884
#> 28043     2  0.0000     0.9155 0.000 1.000
#> 28044     2  0.4939     0.8833 0.108 0.892
#> 28047     2  0.0376     0.9163 0.004 0.996
#> 30001     1  0.3584     0.8991 0.932 0.068
#> 31007     2  0.6887     0.8276 0.184 0.816
#> 31011     2  0.2948     0.9106 0.052 0.948
#> 33005     1  0.0376     0.9054 0.996 0.004
#> 36001     1  0.3114     0.9025 0.944 0.056
#> 36002     2  0.0000     0.9155 0.000 1.000
#> 37013     2  0.7139     0.8149 0.196 0.804
#> 43001     2  0.7139     0.8160 0.196 0.804
#> 43004     2  0.7745     0.7740 0.228 0.772
#> 43007     2  0.0000     0.9155 0.000 1.000
#> 43012     2  0.2043     0.9158 0.032 0.968
#> 48001     1  0.2948     0.9031 0.948 0.052
#> 49006     2  0.0376     0.9162 0.004 0.996
#> 57001     2  0.4161     0.9008 0.084 0.916
#> 62001     2  0.7139     0.7965 0.196 0.804
#> 62002     2  0.5946     0.8665 0.144 0.856
#> 62003     2  0.9983     0.1919 0.476 0.524
#> 63001     2  0.0000     0.9155 0.000 1.000
#> 64001     2  0.0000     0.9155 0.000 1.000
#> 64002     1  0.0376     0.9054 0.996 0.004
#> 65005     2  0.0000     0.9155 0.000 1.000
#> 68001     1  0.0376     0.9054 0.996 0.004
#> 68003     2  0.0376     0.9164 0.004 0.996
#> 84004     2  0.0000     0.9155 0.000 1.000
#> LAL5      2  0.2778     0.9119 0.048 0.952
#> 01003     2  0.5059     0.8823 0.112 0.888
#> 01007     2  0.5629     0.8700 0.132 0.868
#> 02020     2  0.7299     0.8099 0.204 0.796
#> 04018     2  0.5629     0.8700 0.132 0.868
#> 09002     2  0.0376     0.9148 0.004 0.996
#> 10005     2  0.0376     0.9148 0.004 0.996
#> 11002     2  0.0938     0.9159 0.012 0.988
#> 12008     2  0.0938     0.9159 0.012 0.988
#> 15006     1  0.0000     0.9031 1.000 0.000
#> 16002     2  0.2948     0.9099 0.052 0.948
#> 16007     2  0.0376     0.9148 0.004 0.996
#> 17003     2  0.7453     0.8003 0.212 0.788
#> 18001     2  0.0938     0.9159 0.012 0.988
#> 19002     2  0.5629     0.8700 0.132 0.868
#> 19008     2  0.0376     0.9148 0.004 0.996
#> 19014     2  0.7219     0.8145 0.200 0.800
#> 19017     2  0.0672     0.9152 0.008 0.992
#> 20005     2  0.0672     0.9152 0.008 0.992
#> 24006     2  0.5178     0.8804 0.116 0.884
#> 26009     1  0.0000     0.9031 1.000 0.000
#> 28008     2  0.0938     0.9159 0.012 0.988
#> 28009     2  0.5629     0.8700 0.132 0.868
#> 31015     2  0.0938     0.9159 0.012 0.988
#> 37001     2  0.5629     0.8700 0.132 0.868
#> 43006     2  0.0376     0.9148 0.004 0.996
#> 43015     2  0.0938     0.9159 0.012 0.988
#> 44001     2  0.5059     0.8823 0.112 0.888
#> 49004     2  0.0376     0.9148 0.004 0.996
#> 56007     2  0.0376     0.9148 0.004 0.996
#> 64005     2  0.0938     0.9159 0.012 0.988
#> 65003     2  0.5737     0.8681 0.136 0.864
#> 83001     2  0.5519     0.8720 0.128 0.872
#> LAL4      2  0.7219     0.8145 0.200 0.800

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-hclust-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-MAD-hclust-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-MAD-hclust-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-MAD-hclust-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-hclust-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-MAD-hclust-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-hclust-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>              n sex(p) age(p)    BT(p) k
#> MAD:hclust 124  0.350  0.991 2.88e-01 2
#> MAD:hclust 109  0.446  0.958 3.01e-07 3
#> MAD:hclust  73  0.545  0.210 1.20e-08 4
#> MAD:hclust  98  0.515  0.927 2.85e-12 5
#> MAD:hclust  81  0.770  0.777 9.34e-11 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

MAD:kmeans

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk MAD-kmeans-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk MAD-kmeans-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.358           0.822       0.864         0.4173 0.614   0.614
#> 3 3 0.706           0.825       0.879         0.5154 0.689   0.516
#> 4 4 0.838           0.909       0.923         0.1774 0.848   0.602
#> 5 5 0.770           0.703       0.829         0.0601 0.981   0.924
#> 6 6 0.744           0.538       0.726         0.0429 0.972   0.882

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2  0.8207      0.627 0.256 0.744
#> 01010     1  0.4815      0.947 0.896 0.104
#> 03002     2  0.2423      0.846 0.040 0.960
#> 04006     1  0.4815      0.947 0.896 0.104
#> 04007     2  0.2043      0.849 0.032 0.968
#> 04008     1  0.6247      0.913 0.844 0.156
#> 04010     1  0.4815      0.947 0.896 0.104
#> 04016     2  0.2423      0.846 0.040 0.960
#> 06002     2  0.8713      0.564 0.292 0.708
#> 08001     2  0.1633      0.851 0.024 0.976
#> 08011     2  0.8207      0.627 0.256 0.744
#> 08012     2  0.2043      0.849 0.032 0.968
#> 08018     2  0.4562      0.810 0.096 0.904
#> 08024     2  0.8443      0.600 0.272 0.728
#> 09008     1  0.5294      0.940 0.880 0.120
#> 09017     2  0.2236      0.850 0.036 0.964
#> 11005     2  0.1843      0.850 0.028 0.972
#> 12006     2  0.8207      0.627 0.256 0.744
#> 12007     2  0.8207      0.627 0.256 0.744
#> 12012     2  0.8267      0.621 0.260 0.740
#> 12019     2  0.8207      0.627 0.256 0.744
#> 12026     1  0.8443      0.798 0.728 0.272
#> 14016     1  0.8555      0.787 0.720 0.280
#> 15001     2  0.8499      0.593 0.276 0.724
#> 15004     2  0.2043      0.855 0.032 0.968
#> 15005     1  0.5629      0.933 0.868 0.132
#> 16004     1  0.4815      0.947 0.896 0.104
#> 16009     1  0.4815      0.947 0.896 0.104
#> 19005     1  0.4815      0.947 0.896 0.104
#> 20002     1  0.6247      0.913 0.844 0.156
#> 22009     2  0.8386      0.607 0.268 0.732
#> 22010     2  0.4161      0.846 0.084 0.916
#> 22011     2  0.2423      0.846 0.040 0.960
#> 22013     2  0.8813      0.543 0.300 0.700
#> 24001     2  0.2423      0.846 0.040 0.960
#> 24005     2  0.0376      0.856 0.004 0.996
#> 24008     2  0.7299      0.699 0.204 0.796
#> 24010     2  0.4690      0.807 0.100 0.900
#> 24011     2  0.8499      0.593 0.276 0.724
#> 24017     1  0.5519      0.934 0.872 0.128
#> 24018     1  0.5294      0.940 0.880 0.120
#> 24019     1  0.4815      0.947 0.896 0.104
#> 24022     2  0.0376      0.856 0.004 0.996
#> 25003     2  0.6247      0.754 0.156 0.844
#> 25006     1  0.4815      0.947 0.896 0.104
#> 26001     1  0.8555      0.786 0.720 0.280
#> 26003     2  0.0376      0.856 0.004 0.996
#> 26005     2  0.8499      0.593 0.276 0.724
#> 26008     1  0.4815      0.947 0.896 0.104
#> 27003     2  0.1633      0.856 0.024 0.976
#> 27004     2  0.0376      0.856 0.004 0.996
#> 28001     2  0.8713      0.616 0.292 0.708
#> 28003     2  0.3584      0.847 0.068 0.932
#> 28005     2  0.0376      0.856 0.004 0.996
#> 28006     2  0.0376      0.856 0.004 0.996
#> 28007     2  0.0376      0.856 0.004 0.996
#> 28019     1  0.4815      0.947 0.896 0.104
#> 28021     1  0.5408      0.937 0.876 0.124
#> 28023     2  0.2423      0.854 0.040 0.960
#> 28024     2  0.0376      0.856 0.004 0.996
#> 28028     2  0.0000      0.856 0.000 1.000
#> 28031     2  0.3879      0.847 0.076 0.924
#> 28032     2  0.1414      0.856 0.020 0.980
#> 28035     1  0.4815      0.947 0.896 0.104
#> 28036     2  0.0376      0.856 0.004 0.996
#> 28037     1  0.4815      0.947 0.896 0.104
#> 28042     2  0.2043      0.857 0.032 0.968
#> 28043     2  0.0376      0.856 0.004 0.996
#> 28044     2  0.2423      0.854 0.040 0.960
#> 28047     2  0.0938      0.857 0.012 0.988
#> 30001     1  0.4815      0.947 0.896 0.104
#> 31007     2  0.3431      0.849 0.064 0.936
#> 31011     2  0.1184      0.855 0.016 0.984
#> 33005     1  0.4815      0.947 0.896 0.104
#> 36001     1  0.4815      0.947 0.896 0.104
#> 36002     2  0.2423      0.846 0.040 0.960
#> 37013     2  0.8207      0.627 0.256 0.744
#> 43001     1  0.8499      0.794 0.724 0.276
#> 43004     2  0.8713      0.612 0.292 0.708
#> 43007     2  0.2043      0.849 0.032 0.968
#> 43012     2  0.3274      0.850 0.060 0.940
#> 48001     1  0.4815      0.947 0.896 0.104
#> 49006     2  0.7745      0.668 0.228 0.772
#> 57001     2  0.3431      0.849 0.064 0.936
#> 62001     2  0.2423      0.854 0.040 0.960
#> 62002     2  0.1414      0.854 0.020 0.980
#> 62003     1  0.7883      0.823 0.764 0.236
#> 63001     2  0.2236      0.847 0.036 0.964
#> 64001     2  0.8207      0.627 0.256 0.744
#> 64002     1  0.4815      0.947 0.896 0.104
#> 65005     2  0.4431      0.813 0.092 0.908
#> 68001     1  0.4815      0.947 0.896 0.104
#> 68003     2  0.2423      0.846 0.040 0.960
#> 84004     2  0.0000      0.856 0.000 1.000
#> LAL5      2  0.0376      0.856 0.004 0.996
#> 01003     2  0.6247      0.821 0.156 0.844
#> 01007     2  0.6801      0.812 0.180 0.820
#> 02020     2  0.6801      0.812 0.180 0.820
#> 04018     2  0.6623      0.815 0.172 0.828
#> 09002     2  0.5629      0.824 0.132 0.868
#> 10005     2  0.4939      0.827 0.108 0.892
#> 11002     2  0.5737      0.824 0.136 0.864
#> 12008     2  0.6048      0.822 0.148 0.852
#> 15006     1  0.0938      0.829 0.988 0.012
#> 16002     2  0.6247      0.821 0.156 0.844
#> 16007     2  0.6247      0.821 0.156 0.844
#> 17003     1  0.4022      0.795 0.920 0.080
#> 18001     2  0.6247      0.821 0.156 0.844
#> 19002     2  0.6801      0.812 0.180 0.820
#> 19008     2  0.6247      0.821 0.156 0.844
#> 19014     2  0.6801      0.812 0.180 0.820
#> 19017     2  0.5629      0.824 0.132 0.868
#> 20005     2  0.6247      0.821 0.156 0.844
#> 24006     2  0.6801      0.812 0.180 0.820
#> 26009     1  0.0000      0.839 1.000 0.000
#> 28008     2  0.6247      0.821 0.156 0.844
#> 28009     2  0.6801      0.812 0.180 0.820
#> 31015     2  0.6247      0.821 0.156 0.844
#> 37001     2  0.6801      0.812 0.180 0.820
#> 43006     2  0.5629      0.824 0.132 0.868
#> 43015     2  0.6247      0.821 0.156 0.844
#> 44001     2  0.6623      0.815 0.172 0.828
#> 49004     2  0.5629      0.824 0.132 0.868
#> 56007     2  0.6247      0.821 0.156 0.844
#> 64005     2  0.6801      0.812 0.180 0.820
#> 65003     2  0.6623      0.815 0.172 0.828
#> 83001     2  0.6801      0.812 0.180 0.820
#> LAL4      2  0.6623      0.815 0.172 0.828

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-kmeans-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-MAD-kmeans-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-MAD-kmeans-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-MAD-kmeans-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-kmeans-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-MAD-kmeans-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-kmeans-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>              n sex(p) age(p)    BT(p) k
#> MAD:kmeans 128  0.448  0.431 6.90e-02 2
#> MAD:kmeans 125  0.205  0.817 2.29e-07 3
#> MAD:kmeans 126  0.221  0.626 4.90e-20 4
#> MAD:kmeans 111  0.520  0.587 1.87e-17 5
#> MAD:kmeans  88  0.456  0.417 9.08e-13 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

MAD:skmeans**

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk MAD-skmeans-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk MAD-skmeans-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.801           0.880       0.949         0.5009 0.500   0.500
#> 3 3 0.774           0.916       0.947         0.3103 0.748   0.541
#> 4 4 1.000           0.958       0.983         0.1479 0.846   0.587
#> 5 5 0.835           0.728       0.871         0.0592 0.948   0.794
#> 6 6 0.790           0.672       0.781         0.0355 0.959   0.812

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     1  0.0672     0.9625 0.992 0.008
#> 01010     1  0.0000     0.9644 1.000 0.000
#> 03002     1  0.6148     0.8017 0.848 0.152
#> 04006     1  0.0000     0.9644 1.000 0.000
#> 04007     2  0.9323     0.5198 0.348 0.652
#> 04008     1  0.0000     0.9644 1.000 0.000
#> 04010     1  0.0000     0.9644 1.000 0.000
#> 04016     2  0.9993     0.1704 0.484 0.516
#> 06002     1  0.0672     0.9625 0.992 0.008
#> 08001     2  0.7219     0.7484 0.200 0.800
#> 08011     1  0.0672     0.9625 0.992 0.008
#> 08012     2  0.7219     0.7484 0.200 0.800
#> 08018     1  0.0672     0.9625 0.992 0.008
#> 08024     1  0.0672     0.9625 0.992 0.008
#> 09008     1  0.0000     0.9644 1.000 0.000
#> 09017     2  0.9358     0.5177 0.352 0.648
#> 11005     2  0.7219     0.7484 0.200 0.800
#> 12006     1  0.0672     0.9625 0.992 0.008
#> 12007     1  0.0672     0.9625 0.992 0.008
#> 12012     1  0.0672     0.9625 0.992 0.008
#> 12019     1  0.0672     0.9625 0.992 0.008
#> 12026     1  0.0000     0.9644 1.000 0.000
#> 14016     1  0.0000     0.9644 1.000 0.000
#> 15001     1  0.0672     0.9625 0.992 0.008
#> 15004     2  0.0000     0.9276 0.000 1.000
#> 15005     1  0.0000     0.9644 1.000 0.000
#> 16004     1  0.0000     0.9644 1.000 0.000
#> 16009     1  0.0000     0.9644 1.000 0.000
#> 19005     1  0.0000     0.9644 1.000 0.000
#> 20002     1  0.0000     0.9644 1.000 0.000
#> 22009     1  0.0376     0.9635 0.996 0.004
#> 22010     2  0.0672     0.9257 0.008 0.992
#> 22011     2  0.9993     0.1704 0.484 0.516
#> 22013     1  0.0376     0.9635 0.996 0.004
#> 24001     2  0.9993     0.1704 0.484 0.516
#> 24005     2  0.1184     0.9201 0.016 0.984
#> 24008     1  0.0672     0.9625 0.992 0.008
#> 24010     1  0.7299     0.7206 0.796 0.204
#> 24011     1  0.0672     0.9625 0.992 0.008
#> 24017     1  0.0000     0.9644 1.000 0.000
#> 24018     1  0.0000     0.9644 1.000 0.000
#> 24019     1  0.0000     0.9644 1.000 0.000
#> 24022     2  0.0000     0.9276 0.000 1.000
#> 25003     1  0.0672     0.9625 0.992 0.008
#> 25006     1  0.0000     0.9644 1.000 0.000
#> 26001     1  0.0000     0.9644 1.000 0.000
#> 26003     2  0.0000     0.9276 0.000 1.000
#> 26005     1  0.0672     0.9625 0.992 0.008
#> 26008     1  0.0000     0.9644 1.000 0.000
#> 27003     2  0.0672     0.9257 0.008 0.992
#> 27004     2  0.0000     0.9276 0.000 1.000
#> 28001     1  0.5059     0.8575 0.888 0.112
#> 28003     2  0.0672     0.9257 0.008 0.992
#> 28005     2  0.0938     0.9226 0.012 0.988
#> 28006     2  0.0672     0.9247 0.008 0.992
#> 28007     2  0.0672     0.9247 0.008 0.992
#> 28019     1  0.0000     0.9644 1.000 0.000
#> 28021     1  0.0000     0.9644 1.000 0.000
#> 28023     2  0.0000     0.9276 0.000 1.000
#> 28024     2  0.0672     0.9247 0.008 0.992
#> 28028     2  0.0000     0.9276 0.000 1.000
#> 28031     1  0.9922     0.0843 0.552 0.448
#> 28032     2  0.0000     0.9276 0.000 1.000
#> 28035     1  0.6973     0.7598 0.812 0.188
#> 28036     2  0.0000     0.9276 0.000 1.000
#> 28037     1  0.0000     0.9644 1.000 0.000
#> 28042     2  0.0000     0.9276 0.000 1.000
#> 28043     2  0.0000     0.9276 0.000 1.000
#> 28044     2  0.1184     0.9233 0.016 0.984
#> 28047     2  0.0000     0.9276 0.000 1.000
#> 30001     1  0.0000     0.9644 1.000 0.000
#> 31007     2  0.0376     0.9268 0.004 0.996
#> 31011     2  0.3879     0.8746 0.076 0.924
#> 33005     1  0.0000     0.9644 1.000 0.000
#> 36001     1  0.0000     0.9644 1.000 0.000
#> 36002     2  0.9996     0.1564 0.488 0.512
#> 37013     1  0.0376     0.9635 0.996 0.004
#> 43001     1  0.0000     0.9644 1.000 0.000
#> 43004     1  0.0000     0.9644 1.000 0.000
#> 43007     2  0.7299     0.7437 0.204 0.796
#> 43012     2  0.0376     0.9268 0.004 0.996
#> 48001     1  0.0000     0.9644 1.000 0.000
#> 49006     1  0.0672     0.9625 0.992 0.008
#> 57001     2  0.0000     0.9276 0.000 1.000
#> 62001     2  0.1184     0.9233 0.016 0.984
#> 62002     2  0.4161     0.8705 0.084 0.916
#> 62003     1  0.0000     0.9644 1.000 0.000
#> 63001     2  0.9608     0.4435 0.384 0.616
#> 64001     1  0.0672     0.9625 0.992 0.008
#> 64002     1  0.0000     0.9644 1.000 0.000
#> 65005     1  0.0672     0.9625 0.992 0.008
#> 68001     1  0.0000     0.9644 1.000 0.000
#> 68003     2  0.9963     0.2338 0.464 0.536
#> 84004     2  0.4161     0.8678 0.084 0.916
#> LAL5      2  0.0000     0.9276 0.000 1.000
#> 01003     2  0.0000     0.9276 0.000 1.000
#> 01007     2  0.0672     0.9257 0.008 0.992
#> 02020     2  0.0672     0.9257 0.008 0.992
#> 04018     2  0.0376     0.9268 0.004 0.996
#> 09002     2  0.0000     0.9276 0.000 1.000
#> 10005     2  0.0000     0.9276 0.000 1.000
#> 11002     2  0.0000     0.9276 0.000 1.000
#> 12008     2  0.0000     0.9276 0.000 1.000
#> 15006     1  0.7219     0.7436 0.800 0.200
#> 16002     2  0.0000     0.9276 0.000 1.000
#> 16007     2  0.0000     0.9276 0.000 1.000
#> 17003     1  0.7219     0.7436 0.800 0.200
#> 18001     2  0.0000     0.9276 0.000 1.000
#> 19002     2  0.0672     0.9257 0.008 0.992
#> 19008     2  0.0000     0.9276 0.000 1.000
#> 19014     2  0.0672     0.9257 0.008 0.992
#> 19017     2  0.0000     0.9276 0.000 1.000
#> 20005     2  0.0000     0.9276 0.000 1.000
#> 24006     2  0.0672     0.9257 0.008 0.992
#> 26009     1  0.6531     0.7887 0.832 0.168
#> 28008     2  0.0000     0.9276 0.000 1.000
#> 28009     2  0.0672     0.9257 0.008 0.992
#> 31015     2  0.0000     0.9276 0.000 1.000
#> 37001     2  0.0672     0.9257 0.008 0.992
#> 43006     2  0.0000     0.9276 0.000 1.000
#> 43015     2  0.0000     0.9276 0.000 1.000
#> 44001     2  0.0376     0.9268 0.004 0.996
#> 49004     2  0.0000     0.9276 0.000 1.000
#> 56007     2  0.0000     0.9276 0.000 1.000
#> 64005     2  0.0672     0.9257 0.008 0.992
#> 65003     2  0.0672     0.9257 0.008 0.992
#> 83001     2  0.0672     0.9257 0.008 0.992
#> LAL4      2  0.0672     0.9257 0.008 0.992

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-skmeans-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-MAD-skmeans-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-MAD-skmeans-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-MAD-skmeans-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-skmeans-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-MAD-skmeans-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-skmeans-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>               n sex(p) age(p)    BT(p) k
#> MAD:skmeans 121  0.555  0.791 2.66e-06 2
#> MAD:skmeans 128  0.181  0.994 1.47e-07 3
#> MAD:skmeans 126  0.238  0.597 7.68e-19 4
#> MAD:skmeans 103  0.455  0.858 6.71e-14 5
#> MAD:skmeans 106  0.434  0.793 4.34e-15 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

MAD:pam

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk MAD-pam-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk MAD-pam-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.400           0.775       0.824         0.4797 0.497   0.497
#> 3 3 0.625           0.814       0.864         0.3767 0.746   0.531
#> 4 4 0.899           0.885       0.953         0.1294 0.805   0.502
#> 5 5 0.864           0.864       0.935         0.0536 0.935   0.758
#> 6 6 0.841           0.824       0.900         0.0227 0.985   0.930

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2  0.1843      0.818 0.028 0.972
#> 01010     1  0.8813      0.834 0.700 0.300
#> 03002     2  0.2948      0.823 0.052 0.948
#> 04006     1  0.8909      0.832 0.692 0.308
#> 04007     2  0.0672      0.828 0.008 0.992
#> 04008     1  0.9209      0.827 0.664 0.336
#> 04010     1  0.8813      0.834 0.700 0.300
#> 04016     1  1.0000      0.525 0.500 0.500
#> 06002     1  0.8443      0.825 0.728 0.272
#> 08001     2  0.1633      0.838 0.024 0.976
#> 08011     2  0.1843      0.818 0.028 0.972
#> 08012     2  0.2423      0.820 0.040 0.960
#> 08018     2  0.4815      0.807 0.104 0.896
#> 08024     1  0.9286      0.824 0.656 0.344
#> 09008     1  0.8955      0.829 0.688 0.312
#> 09017     2  0.1843      0.839 0.028 0.972
#> 11005     2  0.0000      0.830 0.000 1.000
#> 12006     1  0.9922      0.694 0.552 0.448
#> 12007     2  0.1843      0.818 0.028 0.972
#> 12012     2  0.1843      0.818 0.028 0.972
#> 12019     1  0.9286      0.824 0.656 0.344
#> 12026     1  0.8267      0.820 0.740 0.260
#> 14016     1  0.9286      0.824 0.656 0.344
#> 15001     1  0.9286      0.824 0.656 0.344
#> 15004     2  0.2423      0.836 0.040 0.960
#> 15005     1  0.9000      0.827 0.684 0.316
#> 16004     1  0.7950      0.827 0.760 0.240
#> 16009     1  0.8207      0.820 0.744 0.256
#> 19005     1  0.8813      0.834 0.700 0.300
#> 20002     1  0.9286      0.824 0.656 0.344
#> 22009     1  0.9209      0.826 0.664 0.336
#> 22010     1  0.6801      0.672 0.820 0.180
#> 22011     2  0.1843      0.818 0.028 0.972
#> 22013     1  0.9286      0.824 0.656 0.344
#> 24001     2  0.1843      0.818 0.028 0.972
#> 24005     2  0.1843      0.839 0.028 0.972
#> 24008     2  0.3274      0.782 0.060 0.940
#> 24010     2  0.0376      0.830 0.004 0.996
#> 24011     1  0.9286      0.824 0.656 0.344
#> 24017     1  0.9209      0.827 0.664 0.336
#> 24018     1  0.8861      0.832 0.696 0.304
#> 24019     1  0.4815      0.732 0.896 0.104
#> 24022     2  0.1843      0.839 0.028 0.972
#> 25003     1  0.9427      0.814 0.640 0.360
#> 25006     1  0.7883      0.826 0.764 0.236
#> 26001     1  0.8861      0.831 0.696 0.304
#> 26003     2  0.1843      0.839 0.028 0.972
#> 26005     1  0.9286      0.824 0.656 0.344
#> 26008     1  0.8713      0.830 0.708 0.292
#> 27003     2  0.2236      0.837 0.036 0.964
#> 27004     2  0.1843      0.839 0.028 0.972
#> 28001     1  0.8608      0.814 0.716 0.284
#> 28003     1  0.5059      0.710 0.888 0.112
#> 28005     2  0.1843      0.839 0.028 0.972
#> 28006     2  0.1843      0.839 0.028 0.972
#> 28007     2  0.1843      0.839 0.028 0.972
#> 28019     1  0.8861      0.832 0.696 0.304
#> 28021     1  0.9000      0.827 0.684 0.316
#> 28023     2  0.1843      0.839 0.028 0.972
#> 28024     2  0.1843      0.839 0.028 0.972
#> 28028     2  0.0000      0.830 0.000 1.000
#> 28031     1  0.9248      0.815 0.660 0.340
#> 28032     2  0.1843      0.839 0.028 0.972
#> 28035     1  0.8909      0.831 0.692 0.308
#> 28036     2  0.1843      0.839 0.028 0.972
#> 28037     1  0.8386      0.830 0.732 0.268
#> 28042     2  0.7453      0.757 0.212 0.788
#> 28043     2  0.1843      0.839 0.028 0.972
#> 28044     2  0.1843      0.839 0.028 0.972
#> 28047     2  0.1843      0.839 0.028 0.972
#> 30001     1  0.8909      0.832 0.692 0.308
#> 31007     1  0.8713      0.820 0.708 0.292
#> 31011     2  0.1843      0.839 0.028 0.972
#> 33005     1  0.8499      0.834 0.724 0.276
#> 36001     1  0.8081      0.824 0.752 0.248
#> 36002     2  0.2043      0.820 0.032 0.968
#> 37013     2  0.3114      0.823 0.056 0.944
#> 43001     1  0.9286      0.824 0.656 0.344
#> 43004     1  0.9000      0.827 0.684 0.316
#> 43007     2  0.1843      0.818 0.028 0.972
#> 43012     2  0.5842      0.796 0.140 0.860
#> 48001     1  0.8909      0.831 0.692 0.308
#> 49006     2  0.1843      0.818 0.028 0.972
#> 57001     2  0.6148      0.799 0.152 0.848
#> 62001     2  0.2043      0.837 0.032 0.968
#> 62002     2  0.1843      0.839 0.028 0.972
#> 62003     1  0.9000      0.827 0.684 0.316
#> 63001     2  0.0000      0.830 0.000 1.000
#> 64001     2  0.1843      0.818 0.028 0.972
#> 64002     1  0.8081      0.817 0.752 0.248
#> 65005     2  0.0938      0.827 0.012 0.988
#> 68001     1  0.7602      0.820 0.780 0.220
#> 68003     2  0.0000      0.830 0.000 1.000
#> 84004     2  0.1843      0.839 0.028 0.972
#> LAL5      2  0.5737      0.798 0.136 0.864
#> 01003     2  0.9286      0.682 0.344 0.656
#> 01007     1  0.0000      0.685 1.000 0.000
#> 02020     1  0.0000      0.685 1.000 0.000
#> 04018     2  0.9286      0.682 0.344 0.656
#> 09002     2  0.9170      0.675 0.332 0.668
#> 10005     2  0.8555      0.700 0.280 0.720
#> 11002     2  0.9170      0.689 0.332 0.668
#> 12008     1  0.9866     -0.264 0.568 0.432
#> 15006     1  0.0376      0.685 0.996 0.004
#> 16002     2  0.9286      0.682 0.344 0.656
#> 16007     2  0.9286      0.682 0.344 0.656
#> 17003     1  0.0000      0.685 1.000 0.000
#> 18001     2  0.9286      0.682 0.344 0.656
#> 19002     1  0.0000      0.685 1.000 0.000
#> 19008     2  0.9286      0.682 0.344 0.656
#> 19014     1  0.0000      0.685 1.000 0.000
#> 19017     2  0.9286      0.682 0.344 0.656
#> 20005     2  0.9286      0.682 0.344 0.656
#> 24006     1  0.0000      0.685 1.000 0.000
#> 26009     1  0.0000      0.685 1.000 0.000
#> 28008     2  0.9286      0.682 0.344 0.656
#> 28009     1  0.0000      0.685 1.000 0.000
#> 31015     2  0.9358      0.680 0.352 0.648
#> 37001     1  0.0000      0.685 1.000 0.000
#> 43006     2  0.9000      0.679 0.316 0.684
#> 43015     2  0.9522      0.671 0.372 0.628
#> 44001     2  0.9850      0.607 0.428 0.572
#> 49004     2  0.9000      0.679 0.316 0.684
#> 56007     2  0.9286      0.682 0.344 0.656
#> 64005     1  0.0000      0.685 1.000 0.000
#> 65003     2  0.9286      0.682 0.344 0.656
#> 83001     1  0.0000      0.685 1.000 0.000
#> LAL4      1  0.1843      0.665 0.972 0.028

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-pam-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-MAD-pam-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-MAD-pam-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-MAD-pam-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-pam-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-MAD-pam-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-pam-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>           n sex(p) age(p)    BT(p) k
#> MAD:pam 127  0.745  0.231 4.02e-01 2
#> MAD:pam 127  0.163  0.353 2.04e-03 3
#> MAD:pam 120  0.390  0.941 1.29e-14 4
#> MAD:pam 122  0.414  0.779 8.08e-14 5
#> MAD:pam 120  0.625  0.873 6.31e-13 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

MAD:mclust*

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'mclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk MAD-mclust-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk MAD-mclust-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.524           0.919       0.907         0.3907 0.607   0.607
#> 3 3 0.459           0.635       0.752         0.5883 0.799   0.669
#> 4 4 0.906           0.930       0.966         0.2007 0.849   0.627
#> 5 5 0.822           0.843       0.875         0.0368 1.000   1.000
#> 6 6 0.776           0.682       0.825         0.0365 0.933   0.739

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     1  0.0000      0.914 1.000 0.000
#> 01010     1  0.7453      0.875 0.788 0.212
#> 03002     1  0.0000      0.914 1.000 0.000
#> 04006     1  0.7453      0.875 0.788 0.212
#> 04007     1  0.0376      0.915 0.996 0.004
#> 04008     1  0.0672      0.915 0.992 0.008
#> 04010     1  0.7453      0.875 0.788 0.212
#> 04016     1  0.1843      0.920 0.972 0.028
#> 06002     1  0.0000      0.914 1.000 0.000
#> 08001     1  0.3879      0.925 0.924 0.076
#> 08011     1  0.0000      0.914 1.000 0.000
#> 08012     1  0.0000      0.914 1.000 0.000
#> 08018     1  0.0000      0.914 1.000 0.000
#> 08024     1  0.0000      0.914 1.000 0.000
#> 09008     1  0.7453      0.875 0.788 0.212
#> 09017     1  0.3879      0.925 0.924 0.076
#> 11005     1  0.0000      0.914 1.000 0.000
#> 12006     1  0.0000      0.914 1.000 0.000
#> 12007     1  0.0000      0.914 1.000 0.000
#> 12012     1  0.0000      0.914 1.000 0.000
#> 12019     1  0.0000      0.914 1.000 0.000
#> 12026     1  0.3114      0.910 0.944 0.056
#> 14016     1  0.0672      0.916 0.992 0.008
#> 15001     1  0.0000      0.914 1.000 0.000
#> 15004     1  0.3879      0.925 0.924 0.076
#> 15005     1  0.5629      0.900 0.868 0.132
#> 16004     1  0.7453      0.875 0.788 0.212
#> 16009     1  0.7453      0.875 0.788 0.212
#> 19005     1  0.5629      0.900 0.868 0.132
#> 20002     1  0.4939      0.886 0.892 0.108
#> 22009     1  0.0000      0.914 1.000 0.000
#> 22010     2  0.9393      0.479 0.356 0.644
#> 22011     1  0.0000      0.914 1.000 0.000
#> 22013     1  0.0000      0.914 1.000 0.000
#> 24001     1  0.0938      0.917 0.988 0.012
#> 24005     1  0.3879      0.925 0.924 0.076
#> 24008     1  0.0000      0.914 1.000 0.000
#> 24010     1  0.0000      0.914 1.000 0.000
#> 24011     1  0.0000      0.914 1.000 0.000
#> 24017     1  0.7453      0.875 0.788 0.212
#> 24018     1  0.5629      0.900 0.868 0.132
#> 24019     1  0.7453      0.875 0.788 0.212
#> 24022     1  0.3879      0.925 0.924 0.076
#> 25003     1  0.0000      0.914 1.000 0.000
#> 25006     1  0.7453      0.875 0.788 0.212
#> 26001     1  0.0000      0.914 1.000 0.000
#> 26003     1  0.3879      0.925 0.924 0.076
#> 26005     1  0.0000      0.914 1.000 0.000
#> 26008     1  0.7453      0.875 0.788 0.212
#> 27003     1  0.4939      0.914 0.892 0.108
#> 27004     1  0.3879      0.925 0.924 0.076
#> 28001     1  0.6712      0.868 0.824 0.176
#> 28003     1  0.6623      0.872 0.828 0.172
#> 28005     1  0.3879      0.925 0.924 0.076
#> 28006     1  0.3879      0.925 0.924 0.076
#> 28007     1  0.3879      0.925 0.924 0.076
#> 28019     1  0.7453      0.875 0.788 0.212
#> 28021     1  0.6887      0.888 0.816 0.184
#> 28023     1  0.3879      0.925 0.924 0.076
#> 28024     1  0.3879      0.925 0.924 0.076
#> 28028     1  0.3879      0.925 0.924 0.076
#> 28031     1  0.3879      0.925 0.924 0.076
#> 28032     1  0.5408      0.905 0.876 0.124
#> 28035     1  0.7453      0.875 0.788 0.212
#> 28036     1  0.3879      0.925 0.924 0.076
#> 28037     1  0.7453      0.875 0.788 0.212
#> 28042     1  0.6973      0.855 0.812 0.188
#> 28043     1  0.3879      0.925 0.924 0.076
#> 28044     1  0.3879      0.925 0.924 0.076
#> 28047     1  0.3879      0.925 0.924 0.076
#> 30001     1  0.7453      0.875 0.788 0.212
#> 31007     1  0.6438      0.879 0.836 0.164
#> 31011     1  0.3879      0.925 0.924 0.076
#> 33005     1  0.7453      0.875 0.788 0.212
#> 36001     1  0.7453      0.875 0.788 0.212
#> 36002     1  0.3879      0.925 0.924 0.076
#> 37013     1  0.3879      0.925 0.924 0.076
#> 43001     1  0.0938      0.917 0.988 0.012
#> 43004     1  0.5629      0.900 0.868 0.132
#> 43007     1  0.0000      0.914 1.000 0.000
#> 43012     1  0.5629      0.900 0.868 0.132
#> 48001     1  0.7056      0.885 0.808 0.192
#> 49006     1  0.0000      0.914 1.000 0.000
#> 57001     1  0.4562      0.918 0.904 0.096
#> 62001     1  0.3879      0.925 0.924 0.076
#> 62002     1  0.3879      0.925 0.924 0.076
#> 62003     1  0.5629      0.900 0.868 0.132
#> 63001     1  0.0000      0.914 1.000 0.000
#> 64001     1  0.0000      0.914 1.000 0.000
#> 64002     1  0.7453      0.875 0.788 0.212
#> 65005     1  0.0000      0.914 1.000 0.000
#> 68001     1  0.7453      0.875 0.788 0.212
#> 68003     1  0.0000      0.914 1.000 0.000
#> 84004     1  0.3879      0.925 0.924 0.076
#> LAL5      1  0.5294      0.907 0.880 0.120
#> 01003     2  0.4022      0.980 0.080 0.920
#> 01007     2  0.4022      0.980 0.080 0.920
#> 02020     2  0.4022      0.980 0.080 0.920
#> 04018     2  0.4022      0.980 0.080 0.920
#> 09002     2  0.4022      0.980 0.080 0.920
#> 10005     2  0.7219      0.872 0.200 0.800
#> 11002     2  0.4022      0.980 0.080 0.920
#> 12008     2  0.4022      0.980 0.080 0.920
#> 15006     2  0.2603      0.885 0.044 0.956
#> 16002     2  0.4022      0.980 0.080 0.920
#> 16007     2  0.4022      0.980 0.080 0.920
#> 17003     2  0.4022      0.980 0.080 0.920
#> 18001     2  0.4022      0.980 0.080 0.920
#> 19002     2  0.4022      0.980 0.080 0.920
#> 19008     2  0.4022      0.980 0.080 0.920
#> 19014     2  0.4022      0.980 0.080 0.920
#> 19017     2  0.4022      0.980 0.080 0.920
#> 20005     2  0.4022      0.980 0.080 0.920
#> 24006     2  0.4022      0.980 0.080 0.920
#> 26009     2  0.2603      0.885 0.044 0.956
#> 28008     2  0.4022      0.980 0.080 0.920
#> 28009     2  0.4022      0.980 0.080 0.920
#> 31015     2  0.4022      0.980 0.080 0.920
#> 37001     2  0.4022      0.980 0.080 0.920
#> 43006     2  0.4022      0.980 0.080 0.920
#> 43015     2  0.4022      0.980 0.080 0.920
#> 44001     2  0.4022      0.980 0.080 0.920
#> 49004     2  0.4022      0.980 0.080 0.920
#> 56007     2  0.4022      0.980 0.080 0.920
#> 64005     2  0.4022      0.980 0.080 0.920
#> 65003     2  0.4022      0.980 0.080 0.920
#> 83001     2  0.4022      0.980 0.080 0.920
#> LAL4      2  0.4022      0.980 0.080 0.920

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-mclust-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-MAD-mclust-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-MAD-mclust-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-MAD-mclust-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-mclust-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-MAD-mclust-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-mclust-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>              n sex(p) age(p)    BT(p) k
#> MAD:mclust 127  0.364  0.164 4.90e-23 2
#> MAD:mclust  93  0.121  0.658 1.42e-13 3
#> MAD:mclust 127  0.107  0.564 1.06e-21 4
#> MAD:mclust 124  0.185  0.658 4.90e-21 5
#> MAD:mclust 106  0.565  0.916 2.76e-14 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

MAD:NMF*

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'NMF' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk MAD-NMF-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk MAD-NMF-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.459           0.721       0.880         0.4483 0.545   0.545
#> 3 3 0.812           0.893       0.941         0.4497 0.708   0.511
#> 4 4 0.902           0.898       0.952         0.1525 0.836   0.572
#> 5 5 0.775           0.751       0.868         0.0646 0.907   0.657
#> 6 6 0.727           0.656       0.800         0.0344 0.966   0.840

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     1  0.9850     0.1463 0.572 0.428
#> 01010     1  0.0000     0.8573 1.000 0.000
#> 03002     2  0.9635     0.4712 0.388 0.612
#> 04006     1  0.0000     0.8573 1.000 0.000
#> 04007     2  0.9686     0.4540 0.396 0.604
#> 04008     1  0.0000     0.8573 1.000 0.000
#> 04010     1  0.0000     0.8573 1.000 0.000
#> 04016     2  0.9608     0.4798 0.384 0.616
#> 06002     1  0.9552     0.3138 0.624 0.376
#> 08001     2  0.7219     0.7495 0.200 0.800
#> 08011     1  0.9970    -0.0180 0.532 0.468
#> 08012     2  0.6887     0.7619 0.184 0.816
#> 08018     2  0.7528     0.7351 0.216 0.784
#> 08024     1  0.9608     0.2916 0.616 0.384
#> 09008     1  0.0000     0.8573 1.000 0.000
#> 09017     2  0.7674     0.7267 0.224 0.776
#> 11005     2  0.7219     0.7495 0.200 0.800
#> 12006     2  0.9970     0.2469 0.468 0.532
#> 12007     2  0.9795     0.4055 0.416 0.584
#> 12012     1  1.0000    -0.1376 0.504 0.496
#> 12019     1  0.9970    -0.0181 0.532 0.468
#> 12026     1  0.0000     0.8573 1.000 0.000
#> 14016     1  0.0672     0.8520 0.992 0.008
#> 15001     1  0.7950     0.6010 0.760 0.240
#> 15004     2  0.0938     0.8394 0.012 0.988
#> 15005     1  0.0000     0.8573 1.000 0.000
#> 16004     1  0.0000     0.8573 1.000 0.000
#> 16009     1  0.0000     0.8573 1.000 0.000
#> 19005     1  0.0000     0.8573 1.000 0.000
#> 20002     1  0.0000     0.8573 1.000 0.000
#> 22009     2  0.9795     0.4056 0.416 0.584
#> 22010     2  0.0000     0.8421 0.000 1.000
#> 22011     2  0.9170     0.5764 0.332 0.668
#> 22013     1  0.6247     0.7183 0.844 0.156
#> 24001     2  0.9732     0.4357 0.404 0.596
#> 24005     2  0.6048     0.7852 0.148 0.852
#> 24008     2  0.9775     0.4158 0.412 0.588
#> 24010     2  0.9710     0.4450 0.400 0.600
#> 24011     1  0.9686     0.2559 0.604 0.396
#> 24017     1  0.0000     0.8573 1.000 0.000
#> 24018     1  0.0000     0.8573 1.000 0.000
#> 24019     1  0.0000     0.8573 1.000 0.000
#> 24022     2  0.0000     0.8421 0.000 1.000
#> 25003     2  0.9710     0.4450 0.400 0.600
#> 25006     1  0.0000     0.8573 1.000 0.000
#> 26001     1  0.0000     0.8573 1.000 0.000
#> 26003     2  0.0000     0.8421 0.000 1.000
#> 26005     1  0.8861     0.4837 0.696 0.304
#> 26008     1  0.0000     0.8573 1.000 0.000
#> 27003     2  0.3431     0.8237 0.064 0.936
#> 27004     2  0.0376     0.8413 0.004 0.996
#> 28001     2  0.7219     0.7495 0.200 0.800
#> 28003     2  0.0000     0.8421 0.000 1.000
#> 28005     2  0.6887     0.7617 0.184 0.816
#> 28006     2  0.5408     0.7983 0.124 0.876
#> 28007     2  0.5946     0.7875 0.144 0.856
#> 28019     1  0.0000     0.8573 1.000 0.000
#> 28021     1  0.0000     0.8573 1.000 0.000
#> 28023     2  0.2236     0.8330 0.036 0.964
#> 28024     2  0.5629     0.7941 0.132 0.868
#> 28028     2  0.0000     0.8421 0.000 1.000
#> 28031     2  0.7376     0.7428 0.208 0.792
#> 28032     2  0.0000     0.8421 0.000 1.000
#> 28035     1  0.0000     0.8573 1.000 0.000
#> 28036     2  0.0000     0.8421 0.000 1.000
#> 28037     1  0.0000     0.8573 1.000 0.000
#> 28042     2  0.0000     0.8421 0.000 1.000
#> 28043     2  0.0000     0.8421 0.000 1.000
#> 28044     2  0.7139     0.7527 0.196 0.804
#> 28047     2  0.0000     0.8421 0.000 1.000
#> 30001     1  0.0000     0.8573 1.000 0.000
#> 31007     2  0.3584     0.8225 0.068 0.932
#> 31011     2  0.7219     0.7495 0.200 0.800
#> 33005     1  0.0000     0.8573 1.000 0.000
#> 36001     1  0.0000     0.8573 1.000 0.000
#> 36002     2  0.9732     0.4357 0.404 0.596
#> 37013     2  0.9963     0.2608 0.464 0.536
#> 43001     1  0.0000     0.8573 1.000 0.000
#> 43004     1  0.6623     0.7004 0.828 0.172
#> 43007     2  0.7219     0.7495 0.200 0.800
#> 43012     2  0.0000     0.8421 0.000 1.000
#> 48001     1  0.0000     0.8573 1.000 0.000
#> 49006     2  0.9933     0.3001 0.452 0.548
#> 57001     2  0.1843     0.8354 0.028 0.972
#> 62001     2  0.8016     0.7121 0.244 0.756
#> 62002     2  0.7602     0.7309 0.220 0.780
#> 62003     1  0.0000     0.8573 1.000 0.000
#> 63001     2  0.7376     0.7427 0.208 0.792
#> 64001     1  0.9732     0.2306 0.596 0.404
#> 64002     1  0.0000     0.8573 1.000 0.000
#> 65005     2  0.9710     0.4450 0.400 0.600
#> 68001     1  0.0000     0.8573 1.000 0.000
#> 68003     2  0.8499     0.6625 0.276 0.724
#> 84004     2  0.4939     0.8057 0.108 0.892
#> LAL5      2  0.0000     0.8421 0.000 1.000
#> 01003     2  0.0000     0.8421 0.000 1.000
#> 01007     2  0.0000     0.8421 0.000 1.000
#> 02020     2  0.0000     0.8421 0.000 1.000
#> 04018     2  0.0000     0.8421 0.000 1.000
#> 09002     2  0.0000     0.8421 0.000 1.000
#> 10005     2  0.0000     0.8421 0.000 1.000
#> 11002     2  0.0000     0.8421 0.000 1.000
#> 12008     2  0.0000     0.8421 0.000 1.000
#> 15006     1  0.7219     0.6470 0.800 0.200
#> 16002     2  0.0000     0.8421 0.000 1.000
#> 16007     2  0.0000     0.8421 0.000 1.000
#> 17003     2  0.9866     0.0904 0.432 0.568
#> 18001     2  0.0000     0.8421 0.000 1.000
#> 19002     2  0.0000     0.8421 0.000 1.000
#> 19008     2  0.0000     0.8421 0.000 1.000
#> 19014     2  0.0000     0.8421 0.000 1.000
#> 19017     2  0.0000     0.8421 0.000 1.000
#> 20005     2  0.0000     0.8421 0.000 1.000
#> 24006     2  0.0000     0.8421 0.000 1.000
#> 26009     1  0.7219     0.6470 0.800 0.200
#> 28008     2  0.0000     0.8421 0.000 1.000
#> 28009     2  0.0000     0.8421 0.000 1.000
#> 31015     2  0.0000     0.8421 0.000 1.000
#> 37001     2  0.0000     0.8421 0.000 1.000
#> 43006     2  0.0000     0.8421 0.000 1.000
#> 43015     2  0.0000     0.8421 0.000 1.000
#> 44001     2  0.0000     0.8421 0.000 1.000
#> 49004     2  0.0000     0.8421 0.000 1.000
#> 56007     2  0.0000     0.8421 0.000 1.000
#> 64005     2  0.0000     0.8421 0.000 1.000
#> 65003     2  0.0000     0.8421 0.000 1.000
#> 83001     2  0.0000     0.8421 0.000 1.000
#> LAL4      2  0.0000     0.8421 0.000 1.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-NMF-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-MAD-NMF-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-MAD-NMF-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-MAD-NMF-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-NMF-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-MAD-NMF-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-NMF-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>           n sex(p) age(p)    BT(p) k
#> MAD:NMF 104 0.5323  0.570 9.69e-04 2
#> MAD:NMF 123 0.0924  0.806 1.49e-06 3
#> MAD:NMF 123 0.2875  0.729 1.55e-18 4
#> MAD:NMF 111 0.2734  0.633 9.14e-14 5
#> MAD:NMF 104 0.3512  0.682 6.27e-14 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

ATC:hclust

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'hclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk ATC-hclust-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk ATC-hclust-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.356           0.732       0.830          0.418 0.514   0.514
#> 3 3 0.618           0.763       0.884          0.422 0.799   0.633
#> 4 4 0.548           0.630       0.837          0.118 0.957   0.891
#> 5 5 0.566           0.674       0.806          0.051 0.964   0.899
#> 6 6 0.603           0.606       0.775          0.056 0.943   0.828

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 3

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2  0.8144      0.525 0.252 0.748
#> 01010     1  0.0000      0.698 1.000 0.000
#> 03002     2  0.2043      0.860 0.032 0.968
#> 04006     1  0.0000      0.698 1.000 0.000
#> 04007     2  0.0000      0.875 0.000 1.000
#> 04008     1  0.6247      0.795 0.844 0.156
#> 04010     1  0.0000      0.698 1.000 0.000
#> 04016     2  0.0938      0.871 0.012 0.988
#> 06002     1  0.8713      0.813 0.708 0.292
#> 08001     2  0.0000      0.875 0.000 1.000
#> 08011     2  0.6973      0.657 0.188 0.812
#> 08012     2  0.0938      0.871 0.012 0.988
#> 08018     1  0.8909      0.802 0.692 0.308
#> 08024     1  0.8443      0.821 0.728 0.272
#> 09008     1  0.6247      0.795 0.844 0.156
#> 09017     1  0.9970      0.513 0.532 0.468
#> 11005     2  0.9775     -0.102 0.412 0.588
#> 12006     1  0.8443      0.821 0.728 0.272
#> 12007     2  0.8207      0.515 0.256 0.744
#> 12012     1  0.8763      0.810 0.704 0.296
#> 12019     1  0.8443      0.821 0.728 0.272
#> 12026     1  0.0000      0.698 1.000 0.000
#> 14016     1  0.0000      0.698 1.000 0.000
#> 15001     1  0.9000      0.794 0.684 0.316
#> 15004     1  0.9044      0.792 0.680 0.320
#> 15005     1  0.8499      0.818 0.724 0.276
#> 16004     1  0.0000      0.698 1.000 0.000
#> 16009     1  0.0000      0.698 1.000 0.000
#> 19005     1  0.8327      0.822 0.736 0.264
#> 20002     1  0.6247      0.795 0.844 0.156
#> 22009     1  0.7602      0.820 0.780 0.220
#> 22010     1  0.8909      0.802 0.692 0.308
#> 22011     2  0.2948      0.844 0.052 0.948
#> 22013     1  0.7602      0.820 0.780 0.220
#> 24001     2  0.2948      0.844 0.052 0.948
#> 24005     2  0.0000      0.875 0.000 1.000
#> 24008     2  0.0000      0.875 0.000 1.000
#> 24010     2  0.0000      0.875 0.000 1.000
#> 24011     1  0.8327      0.823 0.736 0.264
#> 24017     1  0.0000      0.698 1.000 0.000
#> 24018     1  0.7602      0.820 0.780 0.220
#> 24019     1  0.0000      0.698 1.000 0.000
#> 24022     2  0.0000      0.875 0.000 1.000
#> 25003     1  0.8955      0.800 0.688 0.312
#> 25006     1  0.0000      0.698 1.000 0.000
#> 26001     1  0.7602      0.820 0.780 0.220
#> 26003     2  0.0000      0.875 0.000 1.000
#> 26005     1  0.8713      0.813 0.708 0.292
#> 26008     1  0.0000      0.698 1.000 0.000
#> 27003     1  0.9044      0.792 0.680 0.320
#> 27004     2  0.0000      0.875 0.000 1.000
#> 28001     1  0.7674      0.821 0.776 0.224
#> 28003     1  0.8443      0.821 0.728 0.272
#> 28005     2  0.0000      0.875 0.000 1.000
#> 28006     2  0.0000      0.875 0.000 1.000
#> 28007     2  0.0000      0.875 0.000 1.000
#> 28019     1  0.0000      0.698 1.000 0.000
#> 28021     1  0.6801      0.805 0.820 0.180
#> 28023     2  0.0000      0.875 0.000 1.000
#> 28024     2  0.0000      0.875 0.000 1.000
#> 28028     2  0.0000      0.875 0.000 1.000
#> 28031     1  0.9044      0.792 0.680 0.320
#> 28032     2  0.0000      0.875 0.000 1.000
#> 28035     1  0.6247      0.795 0.844 0.156
#> 28036     2  0.0000      0.875 0.000 1.000
#> 28037     1  0.6247      0.795 0.844 0.156
#> 28042     1  0.9909      0.582 0.556 0.444
#> 28043     2  0.8267      0.482 0.260 0.740
#> 28044     1  0.9896      0.571 0.560 0.440
#> 28047     2  0.0000      0.875 0.000 1.000
#> 30001     1  0.0000      0.698 1.000 0.000
#> 31007     1  0.8499      0.814 0.724 0.276
#> 31011     2  0.3879      0.819 0.076 0.924
#> 33005     1  0.6247      0.795 0.844 0.156
#> 36001     1  0.7674      0.821 0.776 0.224
#> 36002     2  0.1843      0.862 0.028 0.972
#> 37013     1  0.8499      0.818 0.724 0.276
#> 43001     1  0.8443      0.821 0.728 0.272
#> 43004     1  0.8327      0.823 0.736 0.264
#> 43007     2  0.0376      0.874 0.004 0.996
#> 43012     1  0.9044      0.792 0.680 0.320
#> 48001     1  0.8081      0.823 0.752 0.248
#> 49006     2  0.2778      0.847 0.048 0.952
#> 57001     1  0.9988      0.465 0.520 0.480
#> 62001     2  0.2043      0.860 0.032 0.968
#> 62002     1  0.9988      0.465 0.520 0.480
#> 62003     1  0.7602      0.820 0.780 0.220
#> 63001     2  0.0000      0.875 0.000 1.000
#> 64001     2  0.0000      0.875 0.000 1.000
#> 64002     1  0.0000      0.698 1.000 0.000
#> 65005     2  0.0000      0.875 0.000 1.000
#> 68001     1  0.0000      0.698 1.000 0.000
#> 68003     1  0.9922      0.552 0.552 0.448
#> 84004     2  0.0000      0.875 0.000 1.000
#> LAL5      2  0.9963     -0.308 0.464 0.536
#> 01003     2  0.9993     -0.381 0.484 0.516
#> 01007     1  0.8955      0.799 0.688 0.312
#> 02020     1  0.8144      0.823 0.748 0.252
#> 04018     2  0.9993     -0.381 0.484 0.516
#> 09002     1  0.9954      0.543 0.540 0.460
#> 10005     2  0.0000      0.875 0.000 1.000
#> 11002     2  0.0000      0.875 0.000 1.000
#> 12008     1  0.8861      0.805 0.696 0.304
#> 15006     1  0.0000      0.698 1.000 0.000
#> 16002     2  0.1843      0.863 0.028 0.972
#> 16007     2  0.1843      0.863 0.028 0.972
#> 17003     1  0.8955      0.801 0.688 0.312
#> 18001     2  0.1184      0.869 0.016 0.984
#> 19002     1  0.8443      0.821 0.728 0.272
#> 19008     2  0.8327      0.472 0.264 0.736
#> 19014     1  0.9000      0.795 0.684 0.316
#> 19017     2  0.0672      0.872 0.008 0.992
#> 20005     2  0.0000      0.875 0.000 1.000
#> 24006     1  0.8443      0.821 0.728 0.272
#> 26009     1  0.0000      0.698 1.000 0.000
#> 28008     2  0.0000      0.875 0.000 1.000
#> 28009     1  0.8955      0.798 0.688 0.312
#> 31015     1  0.9608      0.702 0.616 0.384
#> 37001     1  0.8443      0.821 0.728 0.272
#> 43006     2  0.0000      0.875 0.000 1.000
#> 43015     2  0.9866     -0.185 0.432 0.568
#> 44001     1  0.9608      0.702 0.616 0.384
#> 49004     2  0.1843      0.863 0.028 0.972
#> 56007     2  0.9983     -0.354 0.476 0.524
#> 64005     1  0.8386      0.822 0.732 0.268
#> 65003     1  0.9044      0.792 0.680 0.320
#> 83001     1  0.9896      0.571 0.560 0.440
#> LAL4      1  0.9000      0.795 0.684 0.316

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-ATC-hclust-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-ATC-hclust-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-ATC-hclust-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-ATC-hclust-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-hclust-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-ATC-hclust-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-hclust-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>              n sex(p) age(p) BT(p) k
#> ATC:hclust 118  0.787 0.0829 0.883 2
#> ATC:hclust 113  0.924 0.2654 0.730 3
#> ATC:hclust 103  0.745 0.1740 0.948 4
#> ATC:hclust 106  0.960 0.1760 0.669 5
#> ATC:hclust 100  0.987 0.1405 0.762 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

ATC:kmeans**

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk ATC-kmeans-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk ATC-kmeans-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.544           0.745       0.888         0.4389 0.514   0.514
#> 3 3 0.953           0.922       0.947         0.4193 0.668   0.454
#> 4 4 0.720           0.704       0.834         0.1176 0.882   0.712
#> 5 5 0.647           0.523       0.744         0.0787 0.945   0.843
#> 6 6 0.639           0.552       0.718         0.0562 0.870   0.612

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 3

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2  0.0000     0.9101 0.000 1.000
#> 01010     1  0.0000     0.7763 1.000 0.000
#> 03002     2  0.0000     0.9101 0.000 1.000
#> 04006     1  0.0000     0.7763 1.000 0.000
#> 04007     2  0.0000     0.9101 0.000 1.000
#> 04008     1  0.0000     0.7763 1.000 0.000
#> 04010     1  0.0000     0.7763 1.000 0.000
#> 04016     2  0.0000     0.9101 0.000 1.000
#> 06002     1  0.9754     0.5434 0.592 0.408
#> 08001     2  0.0000     0.9101 0.000 1.000
#> 08011     2  0.0000     0.9101 0.000 1.000
#> 08012     2  0.0000     0.9101 0.000 1.000
#> 08018     2  0.1843     0.8833 0.028 0.972
#> 08024     1  0.9815     0.5224 0.580 0.420
#> 09008     1  0.0000     0.7763 1.000 0.000
#> 09017     2  0.1184     0.8954 0.016 0.984
#> 11005     2  0.0000     0.9101 0.000 1.000
#> 12006     1  0.9815     0.5224 0.580 0.420
#> 12007     2  0.0000     0.9101 0.000 1.000
#> 12012     1  0.9815     0.5224 0.580 0.420
#> 12019     1  0.9815     0.5224 0.580 0.420
#> 12026     1  0.0000     0.7763 1.000 0.000
#> 14016     1  0.0000     0.7763 1.000 0.000
#> 15001     2  0.9815     0.0330 0.420 0.580
#> 15004     2  0.8955     0.4069 0.312 0.688
#> 15005     1  0.0000     0.7763 1.000 0.000
#> 16004     1  0.0000     0.7763 1.000 0.000
#> 16009     1  0.0000     0.7763 1.000 0.000
#> 19005     1  0.7219     0.7343 0.800 0.200
#> 20002     1  0.0000     0.7763 1.000 0.000
#> 22009     1  0.9286     0.6234 0.656 0.344
#> 22010     2  0.9754     0.0861 0.408 0.592
#> 22011     2  0.0000     0.9101 0.000 1.000
#> 22013     1  0.9393     0.6110 0.644 0.356
#> 24001     2  0.0000     0.9101 0.000 1.000
#> 24005     2  0.0000     0.9101 0.000 1.000
#> 24008     2  0.0000     0.9101 0.000 1.000
#> 24010     2  0.0000     0.9101 0.000 1.000
#> 24011     1  0.9635     0.5735 0.612 0.388
#> 24017     1  0.0000     0.7763 1.000 0.000
#> 24018     1  0.6343     0.7472 0.840 0.160
#> 24019     1  0.0000     0.7763 1.000 0.000
#> 24022     2  0.0000     0.9101 0.000 1.000
#> 25003     2  0.9944    -0.1304 0.456 0.544
#> 25006     1  0.0000     0.7763 1.000 0.000
#> 26001     1  0.4562     0.7617 0.904 0.096
#> 26003     2  0.0000     0.9101 0.000 1.000
#> 26005     2  0.9970    -0.1802 0.468 0.532
#> 26008     1  0.0000     0.7763 1.000 0.000
#> 27003     2  0.9775     0.0689 0.412 0.588
#> 27004     2  0.0000     0.9101 0.000 1.000
#> 28001     1  0.9580     0.5835 0.620 0.380
#> 28003     1  0.9815     0.5224 0.580 0.420
#> 28005     2  0.0000     0.9101 0.000 1.000
#> 28006     2  0.0000     0.9101 0.000 1.000
#> 28007     2  0.0000     0.9101 0.000 1.000
#> 28019     1  0.0000     0.7763 1.000 0.000
#> 28021     1  0.7745     0.7184 0.772 0.228
#> 28023     2  0.0000     0.9101 0.000 1.000
#> 28024     2  0.0000     0.9101 0.000 1.000
#> 28028     2  0.0000     0.9101 0.000 1.000
#> 28031     2  0.8499     0.4950 0.276 0.724
#> 28032     2  0.0000     0.9101 0.000 1.000
#> 28035     1  0.0000     0.7763 1.000 0.000
#> 28036     2  0.0000     0.9101 0.000 1.000
#> 28037     1  0.0000     0.7763 1.000 0.000
#> 28042     2  0.0000     0.9101 0.000 1.000
#> 28043     2  0.0000     0.9101 0.000 1.000
#> 28044     2  0.0376     0.9069 0.004 0.996
#> 28047     2  0.0000     0.9101 0.000 1.000
#> 30001     1  0.0000     0.7763 1.000 0.000
#> 31007     2  0.7883     0.5794 0.236 0.764
#> 31011     2  0.0000     0.9101 0.000 1.000
#> 33005     1  0.0000     0.7763 1.000 0.000
#> 36001     1  0.7219     0.7343 0.800 0.200
#> 36002     2  0.0000     0.9101 0.000 1.000
#> 37013     1  0.9686     0.5625 0.604 0.396
#> 43001     1  0.8207     0.6989 0.744 0.256
#> 43004     1  0.9686     0.5625 0.604 0.396
#> 43007     2  0.0000     0.9101 0.000 1.000
#> 43012     2  0.4815     0.7941 0.104 0.896
#> 48001     1  0.7219     0.7343 0.800 0.200
#> 49006     2  0.0000     0.9101 0.000 1.000
#> 57001     2  0.0000     0.9101 0.000 1.000
#> 62001     2  0.0000     0.9101 0.000 1.000
#> 62002     2  0.0000     0.9101 0.000 1.000
#> 62003     1  0.7219     0.7343 0.800 0.200
#> 63001     2  0.0000     0.9101 0.000 1.000
#> 64001     2  0.0000     0.9101 0.000 1.000
#> 64002     1  0.0000     0.7763 1.000 0.000
#> 65005     2  0.0000     0.9101 0.000 1.000
#> 68001     1  0.0000     0.7763 1.000 0.000
#> 68003     2  0.0376     0.9069 0.004 0.996
#> 84004     2  0.0000     0.9101 0.000 1.000
#> LAL5      2  0.0000     0.9101 0.000 1.000
#> 01003     2  0.0376     0.9069 0.004 0.996
#> 01007     1  0.9815     0.5224 0.580 0.420
#> 02020     1  0.7056     0.7374 0.808 0.192
#> 04018     2  0.0376     0.9069 0.004 0.996
#> 09002     2  0.0000     0.9101 0.000 1.000
#> 10005     2  0.0000     0.9101 0.000 1.000
#> 11002     2  0.0000     0.9101 0.000 1.000
#> 12008     1  0.9833     0.5128 0.576 0.424
#> 15006     1  0.0000     0.7763 1.000 0.000
#> 16002     2  0.0000     0.9101 0.000 1.000
#> 16007     2  0.0000     0.9101 0.000 1.000
#> 17003     1  0.9881     0.4817 0.564 0.436
#> 18001     2  0.0000     0.9101 0.000 1.000
#> 19002     2  0.9754     0.0861 0.408 0.592
#> 19008     2  0.0000     0.9101 0.000 1.000
#> 19014     2  0.9170     0.3521 0.332 0.668
#> 19017     2  0.0000     0.9101 0.000 1.000
#> 20005     2  0.0000     0.9101 0.000 1.000
#> 24006     1  0.9815     0.5224 0.580 0.420
#> 26009     1  0.0000     0.7763 1.000 0.000
#> 28008     2  0.0000     0.9101 0.000 1.000
#> 28009     2  0.9661     0.1498 0.392 0.608
#> 31015     2  0.0000     0.9101 0.000 1.000
#> 37001     1  0.9795     0.5296 0.584 0.416
#> 43006     2  0.0000     0.9101 0.000 1.000
#> 43015     2  0.0000     0.9101 0.000 1.000
#> 44001     2  0.0000     0.9101 0.000 1.000
#> 49004     2  0.0000     0.9101 0.000 1.000
#> 56007     2  0.0000     0.9101 0.000 1.000
#> 64005     1  0.9661     0.5682 0.608 0.392
#> 65003     2  0.9170     0.3521 0.332 0.668
#> 83001     1  0.9815     0.5224 0.580 0.420
#> LAL4      2  0.9170     0.3521 0.332 0.668

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-ATC-kmeans-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-ATC-kmeans-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-ATC-kmeans-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-ATC-kmeans-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-kmeans-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-ATC-kmeans-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-kmeans-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>              n sex(p) age(p) BT(p) k
#> ATC:kmeans 115  0.499 0.5622 0.380 2
#> ATC:kmeans 124  0.927 0.0336 0.463 3
#> ATC:kmeans 103  0.981 0.1789 0.661 4
#> ATC:kmeans  78  0.982 0.7164 0.899 5
#> ATC:kmeans  77  0.947 0.0195 0.178 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

ATC:skmeans*

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk ATC-skmeans-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk ATC-skmeans-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.972       0.988         0.5041 0.496   0.496
#> 3 3 0.915           0.886       0.954         0.2817 0.814   0.640
#> 4 4 0.720           0.610       0.772         0.1154 0.924   0.794
#> 5 5 0.717           0.574       0.776         0.0762 0.820   0.480
#> 6 6 0.713           0.619       0.764         0.0401 0.901   0.605

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 3
#> attr(,"optional")
#> [1] 2

There is also optional best \(k\) = 2 that is worth to check.

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2   0.000      0.995 0.000 1.000
#> 01010     1   0.000      0.980 1.000 0.000
#> 03002     2   0.000      0.995 0.000 1.000
#> 04006     1   0.000      0.980 1.000 0.000
#> 04007     2   0.000      0.995 0.000 1.000
#> 04008     1   0.000      0.980 1.000 0.000
#> 04010     1   0.000      0.980 1.000 0.000
#> 04016     2   0.000      0.995 0.000 1.000
#> 06002     1   0.000      0.980 1.000 0.000
#> 08001     2   0.000      0.995 0.000 1.000
#> 08011     2   0.000      0.995 0.000 1.000
#> 08012     2   0.000      0.995 0.000 1.000
#> 08018     2   0.184      0.968 0.028 0.972
#> 08024     1   0.000      0.980 1.000 0.000
#> 09008     1   0.000      0.980 1.000 0.000
#> 09017     2   0.000      0.995 0.000 1.000
#> 11005     2   0.000      0.995 0.000 1.000
#> 12006     1   0.000      0.980 1.000 0.000
#> 12007     2   0.000      0.995 0.000 1.000
#> 12012     1   0.000      0.980 1.000 0.000
#> 12019     1   0.000      0.980 1.000 0.000
#> 12026     1   0.000      0.980 1.000 0.000
#> 14016     1   0.000      0.980 1.000 0.000
#> 15001     1   0.000      0.980 1.000 0.000
#> 15004     1   0.163      0.959 0.976 0.024
#> 15005     1   0.000      0.980 1.000 0.000
#> 16004     1   0.000      0.980 1.000 0.000
#> 16009     1   0.000      0.980 1.000 0.000
#> 19005     1   0.000      0.980 1.000 0.000
#> 20002     1   0.000      0.980 1.000 0.000
#> 22009     1   0.000      0.980 1.000 0.000
#> 22010     1   0.000      0.980 1.000 0.000
#> 22011     2   0.000      0.995 0.000 1.000
#> 22013     1   0.000      0.980 1.000 0.000
#> 24001     2   0.000      0.995 0.000 1.000
#> 24005     2   0.000      0.995 0.000 1.000
#> 24008     2   0.000      0.995 0.000 1.000
#> 24010     2   0.000      0.995 0.000 1.000
#> 24011     1   0.000      0.980 1.000 0.000
#> 24017     1   0.000      0.980 1.000 0.000
#> 24018     1   0.000      0.980 1.000 0.000
#> 24019     1   0.000      0.980 1.000 0.000
#> 24022     2   0.000      0.995 0.000 1.000
#> 25003     1   0.000      0.980 1.000 0.000
#> 25006     1   0.000      0.980 1.000 0.000
#> 26001     1   0.000      0.980 1.000 0.000
#> 26003     2   0.000      0.995 0.000 1.000
#> 26005     1   0.000      0.980 1.000 0.000
#> 26008     1   0.000      0.980 1.000 0.000
#> 27003     1   0.000      0.980 1.000 0.000
#> 27004     2   0.000      0.995 0.000 1.000
#> 28001     1   0.000      0.980 1.000 0.000
#> 28003     1   0.000      0.980 1.000 0.000
#> 28005     2   0.000      0.995 0.000 1.000
#> 28006     2   0.000      0.995 0.000 1.000
#> 28007     2   0.000      0.995 0.000 1.000
#> 28019     1   0.000      0.980 1.000 0.000
#> 28021     1   0.456      0.887 0.904 0.096
#> 28023     2   0.000      0.995 0.000 1.000
#> 28024     2   0.000      0.995 0.000 1.000
#> 28028     2   0.000      0.995 0.000 1.000
#> 28031     1   0.955      0.422 0.624 0.376
#> 28032     2   0.000      0.995 0.000 1.000
#> 28035     1   0.000      0.980 1.000 0.000
#> 28036     2   0.000      0.995 0.000 1.000
#> 28037     1   0.000      0.980 1.000 0.000
#> 28042     2   0.000      0.995 0.000 1.000
#> 28043     2   0.000      0.995 0.000 1.000
#> 28044     2   0.373      0.920 0.072 0.928
#> 28047     2   0.000      0.995 0.000 1.000
#> 30001     1   0.000      0.980 1.000 0.000
#> 31007     1   0.900      0.558 0.684 0.316
#> 31011     2   0.000      0.995 0.000 1.000
#> 33005     1   0.000      0.980 1.000 0.000
#> 36001     1   0.000      0.980 1.000 0.000
#> 36002     2   0.000      0.995 0.000 1.000
#> 37013     1   0.000      0.980 1.000 0.000
#> 43001     1   0.000      0.980 1.000 0.000
#> 43004     1   0.000      0.980 1.000 0.000
#> 43007     2   0.000      0.995 0.000 1.000
#> 43012     2   0.680      0.774 0.180 0.820
#> 48001     1   0.000      0.980 1.000 0.000
#> 49006     2   0.000      0.995 0.000 1.000
#> 57001     2   0.000      0.995 0.000 1.000
#> 62001     2   0.000      0.995 0.000 1.000
#> 62002     2   0.000      0.995 0.000 1.000
#> 62003     1   0.000      0.980 1.000 0.000
#> 63001     2   0.000      0.995 0.000 1.000
#> 64001     2   0.000      0.995 0.000 1.000
#> 64002     1   0.000      0.980 1.000 0.000
#> 65005     2   0.000      0.995 0.000 1.000
#> 68001     1   0.000      0.980 1.000 0.000
#> 68003     2   0.000      0.995 0.000 1.000
#> 84004     2   0.000      0.995 0.000 1.000
#> LAL5      2   0.000      0.995 0.000 1.000
#> 01003     2   0.000      0.995 0.000 1.000
#> 01007     1   0.000      0.980 1.000 0.000
#> 02020     1   0.000      0.980 1.000 0.000
#> 04018     2   0.000      0.995 0.000 1.000
#> 09002     2   0.000      0.995 0.000 1.000
#> 10005     2   0.000      0.995 0.000 1.000
#> 11002     2   0.000      0.995 0.000 1.000
#> 12008     1   0.000      0.980 1.000 0.000
#> 15006     1   0.000      0.980 1.000 0.000
#> 16002     2   0.000      0.995 0.000 1.000
#> 16007     2   0.000      0.995 0.000 1.000
#> 17003     1   0.000      0.980 1.000 0.000
#> 18001     2   0.000      0.995 0.000 1.000
#> 19002     1   0.000      0.980 1.000 0.000
#> 19008     2   0.000      0.995 0.000 1.000
#> 19014     1   0.730      0.753 0.796 0.204
#> 19017     2   0.000      0.995 0.000 1.000
#> 20005     2   0.000      0.995 0.000 1.000
#> 24006     1   0.000      0.980 1.000 0.000
#> 26009     1   0.000      0.980 1.000 0.000
#> 28008     2   0.000      0.995 0.000 1.000
#> 28009     1   0.000      0.980 1.000 0.000
#> 31015     2   0.000      0.995 0.000 1.000
#> 37001     1   0.000      0.980 1.000 0.000
#> 43006     2   0.000      0.995 0.000 1.000
#> 43015     2   0.000      0.995 0.000 1.000
#> 44001     2   0.000      0.995 0.000 1.000
#> 49004     2   0.000      0.995 0.000 1.000
#> 56007     2   0.000      0.995 0.000 1.000
#> 64005     1   0.000      0.980 1.000 0.000
#> 65003     1   0.456      0.888 0.904 0.096
#> 83001     1   0.000      0.980 1.000 0.000
#> LAL4      1   0.689      0.781 0.816 0.184

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-ATC-skmeans-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-ATC-skmeans-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-ATC-skmeans-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-ATC-skmeans-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-skmeans-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-ATC-skmeans-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-skmeans-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>               n sex(p) age(p)  BT(p) k
#> ATC:skmeans 127  0.569 0.3674 0.4547 2
#> ATC:skmeans 117  0.920 0.0211 0.1072 3
#> ATC:skmeans  84  0.999 0.4114 0.5993 4
#> ATC:skmeans  84  0.587 0.0299 0.0548 5
#> ATC:skmeans  95  0.876 0.0727 0.0510 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

ATC:pam**

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 2.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk ATC-pam-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk ATC-pam-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.968       0.981         0.2985 0.703   0.703
#> 3 3 0.661           0.794       0.892         1.0333 0.646   0.508
#> 4 4 0.716           0.798       0.874         0.1977 0.780   0.493
#> 5 5 0.811           0.772       0.896         0.0449 0.880   0.610
#> 6 6 0.769           0.707       0.852         0.0592 0.910   0.648

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 2

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2  0.0000      0.982 0.000 1.000
#> 01010     1  0.0000      0.966 1.000 0.000
#> 03002     2  0.0000      0.982 0.000 1.000
#> 04006     1  0.0000      0.966 1.000 0.000
#> 04007     2  0.0000      0.982 0.000 1.000
#> 04008     1  0.9248      0.481 0.660 0.340
#> 04010     1  0.0000      0.966 1.000 0.000
#> 04016     2  0.0000      0.982 0.000 1.000
#> 06002     2  0.2423      0.974 0.040 0.960
#> 08001     2  0.0000      0.982 0.000 1.000
#> 08011     2  0.0000      0.982 0.000 1.000
#> 08012     2  0.0000      0.982 0.000 1.000
#> 08018     2  0.2423      0.974 0.040 0.960
#> 08024     2  0.2423      0.974 0.040 0.960
#> 09008     1  0.0000      0.966 1.000 0.000
#> 09017     2  0.0376      0.982 0.004 0.996
#> 11005     2  0.0000      0.982 0.000 1.000
#> 12006     2  0.2423      0.974 0.040 0.960
#> 12007     2  0.0000      0.982 0.000 1.000
#> 12012     2  0.2423      0.974 0.040 0.960
#> 12019     2  0.2423      0.974 0.040 0.960
#> 12026     1  0.0376      0.963 0.996 0.004
#> 14016     1  0.0000      0.966 1.000 0.000
#> 15001     2  0.2423      0.974 0.040 0.960
#> 15004     2  0.2423      0.974 0.040 0.960
#> 15005     2  0.2423      0.974 0.040 0.960
#> 16004     1  0.0000      0.966 1.000 0.000
#> 16009     1  0.0000      0.966 1.000 0.000
#> 19005     2  0.2423      0.974 0.040 0.960
#> 20002     1  0.9552      0.393 0.624 0.376
#> 22009     2  0.2423      0.974 0.040 0.960
#> 22010     2  0.2423      0.974 0.040 0.960
#> 22011     2  0.0000      0.982 0.000 1.000
#> 22013     2  0.2423      0.974 0.040 0.960
#> 24001     2  0.0000      0.982 0.000 1.000
#> 24005     2  0.0000      0.982 0.000 1.000
#> 24008     2  0.0000      0.982 0.000 1.000
#> 24010     2  0.0000      0.982 0.000 1.000
#> 24011     2  0.2423      0.974 0.040 0.960
#> 24017     1  0.0000      0.966 1.000 0.000
#> 24018     2  0.2423      0.974 0.040 0.960
#> 24019     1  0.0000      0.966 1.000 0.000
#> 24022     2  0.0000      0.982 0.000 1.000
#> 25003     2  0.2423      0.974 0.040 0.960
#> 25006     1  0.0000      0.966 1.000 0.000
#> 26001     2  0.2423      0.974 0.040 0.960
#> 26003     2  0.0000      0.982 0.000 1.000
#> 26005     2  0.2423      0.974 0.040 0.960
#> 26008     1  0.0000      0.966 1.000 0.000
#> 27003     2  0.2423      0.974 0.040 0.960
#> 27004     2  0.0000      0.982 0.000 1.000
#> 28001     2  0.2423      0.974 0.040 0.960
#> 28003     2  0.2423      0.974 0.040 0.960
#> 28005     2  0.0000      0.982 0.000 1.000
#> 28006     2  0.0000      0.982 0.000 1.000
#> 28007     2  0.0000      0.982 0.000 1.000
#> 28019     1  0.0000      0.966 1.000 0.000
#> 28021     2  0.0376      0.980 0.004 0.996
#> 28023     2  0.0000      0.982 0.000 1.000
#> 28024     2  0.0000      0.982 0.000 1.000
#> 28028     2  0.0000      0.982 0.000 1.000
#> 28031     2  0.2423      0.974 0.040 0.960
#> 28032     2  0.0000      0.982 0.000 1.000
#> 28035     1  0.0000      0.966 1.000 0.000
#> 28036     2  0.0000      0.982 0.000 1.000
#> 28037     1  0.0000      0.966 1.000 0.000
#> 28042     2  0.2423      0.974 0.040 0.960
#> 28043     2  0.0000      0.982 0.000 1.000
#> 28044     2  0.0000      0.982 0.000 1.000
#> 28047     2  0.0000      0.982 0.000 1.000
#> 30001     1  0.0000      0.966 1.000 0.000
#> 31007     2  0.2423      0.974 0.040 0.960
#> 31011     2  0.0000      0.982 0.000 1.000
#> 33005     1  0.0000      0.966 1.000 0.000
#> 36001     2  0.2423      0.974 0.040 0.960
#> 36002     2  0.0000      0.982 0.000 1.000
#> 37013     2  0.2423      0.974 0.040 0.960
#> 43001     2  0.2423      0.974 0.040 0.960
#> 43004     2  0.2423      0.974 0.040 0.960
#> 43007     2  0.0000      0.982 0.000 1.000
#> 43012     2  0.0000      0.982 0.000 1.000
#> 48001     2  0.2423      0.974 0.040 0.960
#> 49006     2  0.0000      0.982 0.000 1.000
#> 57001     2  0.0000      0.982 0.000 1.000
#> 62001     2  0.0000      0.982 0.000 1.000
#> 62002     2  0.0000      0.982 0.000 1.000
#> 62003     2  0.2423      0.974 0.040 0.960
#> 63001     2  0.0000      0.982 0.000 1.000
#> 64001     2  0.0000      0.982 0.000 1.000
#> 64002     1  0.0000      0.966 1.000 0.000
#> 65005     2  0.0000      0.982 0.000 1.000
#> 68001     1  0.0000      0.966 1.000 0.000
#> 68003     2  0.0000      0.982 0.000 1.000
#> 84004     2  0.0000      0.982 0.000 1.000
#> LAL5      2  0.0000      0.982 0.000 1.000
#> 01003     2  0.0000      0.982 0.000 1.000
#> 01007     2  0.2423      0.974 0.040 0.960
#> 02020     2  0.2423      0.974 0.040 0.960
#> 04018     2  0.0000      0.982 0.000 1.000
#> 09002     2  0.0000      0.982 0.000 1.000
#> 10005     2  0.0000      0.982 0.000 1.000
#> 11002     2  0.0000      0.982 0.000 1.000
#> 12008     2  0.2423      0.974 0.040 0.960
#> 15006     1  0.0000      0.966 1.000 0.000
#> 16002     2  0.0000      0.982 0.000 1.000
#> 16007     2  0.0000      0.982 0.000 1.000
#> 17003     2  0.2423      0.974 0.040 0.960
#> 18001     2  0.0000      0.982 0.000 1.000
#> 19002     2  0.2423      0.974 0.040 0.960
#> 19008     2  0.0000      0.982 0.000 1.000
#> 19014     2  0.2423      0.974 0.040 0.960
#> 19017     2  0.0000      0.982 0.000 1.000
#> 20005     2  0.0000      0.982 0.000 1.000
#> 24006     2  0.2423      0.974 0.040 0.960
#> 26009     1  0.0000      0.966 1.000 0.000
#> 28008     2  0.0000      0.982 0.000 1.000
#> 28009     2  0.2423      0.974 0.040 0.960
#> 31015     2  0.0000      0.982 0.000 1.000
#> 37001     2  0.2423      0.974 0.040 0.960
#> 43006     2  0.0000      0.982 0.000 1.000
#> 43015     2  0.0000      0.982 0.000 1.000
#> 44001     2  0.2423      0.974 0.040 0.960
#> 49004     2  0.0000      0.982 0.000 1.000
#> 56007     2  0.0000      0.982 0.000 1.000
#> 64005     2  0.2423      0.974 0.040 0.960
#> 65003     2  0.2423      0.974 0.040 0.960
#> 83001     2  0.0000      0.982 0.000 1.000
#> LAL4      2  0.2423      0.974 0.040 0.960

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-ATC-pam-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-ATC-pam-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-ATC-pam-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-ATC-pam-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-pam-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-ATC-pam-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-pam-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>           n sex(p) age(p) BT(p) k
#> ATC:pam 126  1.000  0.824 0.474 2
#> ATC:pam 122  0.847  0.125 0.668 3
#> ATC:pam 114  0.565  0.479 0.417 4
#> ATC:pam 115  0.840  0.196 0.465 5
#> ATC:pam 106  0.712  0.367 0.433 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

ATC:mclust

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'mclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 2.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk ATC-mclust-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk ATC-mclust-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.859           0.909       0.947         0.4296 0.567   0.567
#> 3 3 0.564           0.752       0.882         0.1680 0.781   0.671
#> 4 4 0.859           0.906       0.956         0.3629 0.714   0.502
#> 5 5 0.881           0.865       0.925         0.0933 0.938   0.806
#> 6 6 0.797           0.778       0.874         0.0583 0.945   0.792

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 2

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2  0.3274     0.9397 0.060 0.940
#> 01010     1  0.2948     0.9276 0.948 0.052
#> 03002     2  0.3114     0.9416 0.056 0.944
#> 04006     1  0.2948     0.9276 0.948 0.052
#> 04007     2  0.3114     0.9416 0.056 0.944
#> 04008     1  0.2948     0.9276 0.948 0.052
#> 04010     1  0.2948     0.9276 0.948 0.052
#> 04016     2  0.3114     0.9416 0.056 0.944
#> 06002     2  0.6247     0.8502 0.156 0.844
#> 08001     2  0.2778     0.9439 0.048 0.952
#> 08011     2  0.3584     0.9358 0.068 0.932
#> 08012     2  0.3114     0.9416 0.056 0.944
#> 08018     2  0.3114     0.9416 0.056 0.944
#> 08024     1  0.9815     0.2616 0.580 0.420
#> 09008     1  0.2948     0.9276 0.948 0.052
#> 09017     2  0.0000     0.9578 0.000 1.000
#> 11005     2  0.0000     0.9578 0.000 1.000
#> 12006     2  0.9993     0.0587 0.484 0.516
#> 12007     2  0.0000     0.9578 0.000 1.000
#> 12012     1  0.8016     0.6884 0.756 0.244
#> 12019     2  0.0672     0.9559 0.008 0.992
#> 12026     2  0.7950     0.6479 0.240 0.760
#> 14016     1  0.6887     0.7919 0.816 0.184
#> 15001     2  0.9996     0.0803 0.488 0.512
#> 15004     2  0.0000     0.9578 0.000 1.000
#> 15005     2  0.6343     0.7815 0.160 0.840
#> 16004     1  0.5737     0.8482 0.864 0.136
#> 16009     1  0.2948     0.9276 0.948 0.052
#> 19005     1  0.2603     0.9144 0.956 0.044
#> 20002     1  0.2948     0.9276 0.948 0.052
#> 22009     2  0.0000     0.9578 0.000 1.000
#> 22010     2  0.0000     0.9578 0.000 1.000
#> 22011     2  0.3114     0.9416 0.056 0.944
#> 22013     2  0.0000     0.9578 0.000 1.000
#> 24001     2  0.3114     0.9416 0.056 0.944
#> 24005     2  0.3114     0.9416 0.056 0.944
#> 24008     1  0.2236     0.9120 0.964 0.036
#> 24010     1  0.2236     0.9120 0.964 0.036
#> 24011     1  0.2236     0.9120 0.964 0.036
#> 24017     1  0.2948     0.9276 0.948 0.052
#> 24018     2  0.0000     0.9578 0.000 1.000
#> 24019     1  0.2948     0.9276 0.948 0.052
#> 24022     2  0.0000     0.9578 0.000 1.000
#> 25003     2  0.0000     0.9578 0.000 1.000
#> 25006     1  0.2948     0.9276 0.948 0.052
#> 26001     2  0.0376     0.9561 0.004 0.996
#> 26003     2  0.0000     0.9578 0.000 1.000
#> 26005     2  0.6343     0.8445 0.160 0.840
#> 26008     1  0.2948     0.9276 0.948 0.052
#> 27003     2  0.0000     0.9578 0.000 1.000
#> 27004     2  0.2948     0.9422 0.052 0.948
#> 28001     1  0.5737     0.8482 0.864 0.136
#> 28003     2  0.0000     0.9578 0.000 1.000
#> 28005     2  0.2948     0.9422 0.052 0.948
#> 28006     1  0.2236     0.9120 0.964 0.036
#> 28007     2  0.2948     0.9422 0.052 0.948
#> 28019     1  0.2948     0.9276 0.948 0.052
#> 28021     1  0.2948     0.9276 0.948 0.052
#> 28023     2  0.2948     0.9422 0.052 0.948
#> 28024     2  0.2948     0.9422 0.052 0.948
#> 28028     2  0.0000     0.9578 0.000 1.000
#> 28031     2  0.3114     0.9416 0.056 0.944
#> 28032     2  0.0000     0.9578 0.000 1.000
#> 28035     1  0.2948     0.9276 0.948 0.052
#> 28036     2  0.0000     0.9578 0.000 1.000
#> 28037     1  0.2948     0.9276 0.948 0.052
#> 28042     2  0.0000     0.9578 0.000 1.000
#> 28043     2  0.0000     0.9578 0.000 1.000
#> 28044     2  0.0000     0.9578 0.000 1.000
#> 28047     2  0.3114     0.9416 0.056 0.944
#> 30001     1  0.2948     0.9276 0.948 0.052
#> 31007     1  0.5737     0.8482 0.864 0.136
#> 31011     2  0.2948     0.9422 0.052 0.948
#> 33005     1  0.2948     0.9276 0.948 0.052
#> 36001     1  0.6531     0.8629 0.832 0.168
#> 36002     2  0.3114     0.9416 0.056 0.944
#> 37013     2  0.0000     0.9578 0.000 1.000
#> 43001     1  0.9170     0.5291 0.668 0.332
#> 43004     2  0.0000     0.9578 0.000 1.000
#> 43007     2  0.3114     0.9416 0.056 0.944
#> 43012     2  0.0000     0.9578 0.000 1.000
#> 48001     2  0.0000     0.9578 0.000 1.000
#> 49006     2  0.5629     0.8770 0.132 0.868
#> 57001     2  0.0000     0.9578 0.000 1.000
#> 62001     2  0.3114     0.9416 0.056 0.944
#> 62002     2  0.0000     0.9578 0.000 1.000
#> 62003     2  0.0000     0.9578 0.000 1.000
#> 63001     1  0.2236     0.9120 0.964 0.036
#> 64001     2  0.3114     0.9416 0.056 0.944
#> 64002     1  0.2948     0.9276 0.948 0.052
#> 65005     2  0.3114     0.9416 0.056 0.944
#> 68001     1  0.2948     0.9276 0.948 0.052
#> 68003     2  0.0000     0.9578 0.000 1.000
#> 84004     2  0.3114     0.9416 0.056 0.944
#> LAL5      2  0.0000     0.9578 0.000 1.000
#> 01003     2  0.0000     0.9578 0.000 1.000
#> 01007     2  0.0000     0.9578 0.000 1.000
#> 02020     2  0.0000     0.9578 0.000 1.000
#> 04018     2  0.0000     0.9578 0.000 1.000
#> 09002     2  0.0000     0.9578 0.000 1.000
#> 10005     1  0.2236     0.9120 0.964 0.036
#> 11002     1  0.2236     0.9120 0.964 0.036
#> 12008     2  0.0000     0.9578 0.000 1.000
#> 15006     1  0.2948     0.9276 0.948 0.052
#> 16002     2  0.0672     0.9559 0.008 0.992
#> 16007     2  0.3114     0.9416 0.056 0.944
#> 17003     1  0.5737     0.8482 0.864 0.136
#> 18001     2  0.2948     0.9422 0.052 0.948
#> 19002     2  0.0000     0.9578 0.000 1.000
#> 19008     2  0.0000     0.9578 0.000 1.000
#> 19014     2  0.0000     0.9578 0.000 1.000
#> 19017     2  0.3114     0.9416 0.056 0.944
#> 20005     2  0.0000     0.9578 0.000 1.000
#> 24006     2  0.0000     0.9578 0.000 1.000
#> 26009     1  0.2948     0.9276 0.948 0.052
#> 28008     1  0.2236     0.9120 0.964 0.036
#> 28009     2  0.0000     0.9578 0.000 1.000
#> 31015     2  0.3274     0.9399 0.060 0.940
#> 37001     2  0.0000     0.9578 0.000 1.000
#> 43006     2  0.0000     0.9578 0.000 1.000
#> 43015     2  0.0000     0.9578 0.000 1.000
#> 44001     1  0.4022     0.8913 0.920 0.080
#> 49004     2  0.0000     0.9578 0.000 1.000
#> 56007     2  0.0000     0.9578 0.000 1.000
#> 64005     2  0.0000     0.9578 0.000 1.000
#> 65003     2  0.0000     0.9578 0.000 1.000
#> 83001     2  0.0000     0.9578 0.000 1.000
#> LAL4      2  0.0000     0.9578 0.000 1.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-ATC-mclust-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-ATC-mclust-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-ATC-mclust-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-ATC-mclust-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-mclust-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-ATC-mclust-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-mclust-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>              n sex(p) age(p)  BT(p) k
#> ATC:mclust 125  0.320  0.893 0.0548 2
#> ATC:mclust 112  0.550  0.160 0.7515 3
#> ATC:mclust 124  0.750  0.109 0.3928 4
#> ATC:mclust 122  0.844  0.165 0.2538 5
#> ATC:mclust 111  0.921  0.418 0.6004 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

ATC:NMF

The object with results only for a single top-value method and a single partition method can be extracted as:

res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]

A summary of res and all the functions that can be applied to it:

res

#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#>   On a matrix with 11993 rows and 128 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'NMF' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 2.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk ATC-NMF-collect-plots

The plots are:

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

The detailed explanations of these statistics can be found in the cola vignette.

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

plot of chunk ATC-NMF-select-partition-number

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.830           0.910       0.962         0.4942 0.502   0.502
#> 3 3 0.618           0.783       0.893         0.3436 0.731   0.510
#> 4 4 0.569           0.540       0.763         0.1155 0.786   0.472
#> 5 5 0.592           0.523       0.708         0.0685 0.802   0.409
#> 6 6 0.636           0.579       0.703         0.0371 0.872   0.495

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

suggest_best_k(res)

#> [1] 2

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>       class entropy silhouette    p1    p2
#> 01005     2  0.8144      0.679 0.252 0.748
#> 01010     1  0.0000      0.963 1.000 0.000
#> 03002     2  0.0376      0.952 0.004 0.996
#> 04006     1  0.0000      0.963 1.000 0.000
#> 04007     2  0.0000      0.954 0.000 1.000
#> 04008     1  0.0000      0.963 1.000 0.000
#> 04010     1  0.0000      0.963 1.000 0.000
#> 04016     2  0.0000      0.954 0.000 1.000
#> 06002     1  0.0000      0.963 1.000 0.000
#> 08001     2  0.0000      0.954 0.000 1.000
#> 08011     2  0.5737      0.840 0.136 0.864
#> 08012     2  0.0000      0.954 0.000 1.000
#> 08018     1  0.9209      0.492 0.664 0.336
#> 08024     1  0.0000      0.963 1.000 0.000
#> 09008     1  0.0000      0.963 1.000 0.000
#> 09017     1  0.0000      0.963 1.000 0.000
#> 11005     2  0.0000      0.954 0.000 1.000
#> 12006     1  0.0000      0.963 1.000 0.000
#> 12007     1  0.7139      0.743 0.804 0.196
#> 12012     1  0.0000      0.963 1.000 0.000
#> 12019     1  0.0000      0.963 1.000 0.000
#> 12026     1  0.0000      0.963 1.000 0.000
#> 14016     1  0.0000      0.963 1.000 0.000
#> 15001     1  0.0000      0.963 1.000 0.000
#> 15004     1  0.7950      0.676 0.760 0.240
#> 15005     1  0.0000      0.963 1.000 0.000
#> 16004     1  0.0000      0.963 1.000 0.000
#> 16009     1  0.0000      0.963 1.000 0.000
#> 19005     1  0.0000      0.963 1.000 0.000
#> 20002     1  0.0000      0.963 1.000 0.000
#> 22009     1  0.0000      0.963 1.000 0.000
#> 22010     1  0.0000      0.963 1.000 0.000
#> 22011     2  0.0000      0.954 0.000 1.000
#> 22013     1  0.0000      0.963 1.000 0.000
#> 24001     2  0.0000      0.954 0.000 1.000
#> 24005     2  0.0000      0.954 0.000 1.000
#> 24008     2  0.0376      0.952 0.004 0.996
#> 24010     2  0.0000      0.954 0.000 1.000
#> 24011     1  0.0000      0.963 1.000 0.000
#> 24017     1  0.0000      0.963 1.000 0.000
#> 24018     1  0.0000      0.963 1.000 0.000
#> 24019     1  0.0000      0.963 1.000 0.000
#> 24022     2  0.0000      0.954 0.000 1.000
#> 25003     1  0.0000      0.963 1.000 0.000
#> 25006     1  0.0000      0.963 1.000 0.000
#> 26001     1  0.0000      0.963 1.000 0.000
#> 26003     2  0.0000      0.954 0.000 1.000
#> 26005     1  0.0000      0.963 1.000 0.000
#> 26008     1  0.0000      0.963 1.000 0.000
#> 27003     1  0.0000      0.963 1.000 0.000
#> 27004     2  0.0000      0.954 0.000 1.000
#> 28001     1  0.0000      0.963 1.000 0.000
#> 28003     1  0.0000      0.963 1.000 0.000
#> 28005     2  0.0000      0.954 0.000 1.000
#> 28006     2  0.0000      0.954 0.000 1.000
#> 28007     2  0.0000      0.954 0.000 1.000
#> 28019     1  0.0000      0.963 1.000 0.000
#> 28021     1  0.0000      0.963 1.000 0.000
#> 28023     2  0.0000      0.954 0.000 1.000
#> 28024     2  0.0000      0.954 0.000 1.000
#> 28028     2  0.0000      0.954 0.000 1.000
#> 28031     1  0.0376      0.959 0.996 0.004
#> 28032     2  0.0000      0.954 0.000 1.000
#> 28035     1  0.0000      0.963 1.000 0.000
#> 28036     2  0.0000      0.954 0.000 1.000
#> 28037     1  0.0000      0.963 1.000 0.000
#> 28042     2  0.2236      0.929 0.036 0.964
#> 28043     2  0.0000      0.954 0.000 1.000
#> 28044     1  0.0000      0.963 1.000 0.000
#> 28047     2  0.0000      0.954 0.000 1.000
#> 30001     1  0.0000      0.963 1.000 0.000
#> 31007     1  0.9209      0.492 0.664 0.336
#> 31011     2  0.5178      0.861 0.116 0.884
#> 33005     1  0.0000      0.963 1.000 0.000
#> 36001     1  0.0000      0.963 1.000 0.000
#> 36002     2  0.0000      0.954 0.000 1.000
#> 37013     1  0.0000      0.963 1.000 0.000
#> 43001     1  0.0000      0.963 1.000 0.000
#> 43004     1  0.0000      0.963 1.000 0.000
#> 43007     2  0.0000      0.954 0.000 1.000
#> 43012     2  0.9977      0.119 0.472 0.528
#> 48001     1  0.0000      0.963 1.000 0.000
#> 49006     2  0.0000      0.954 0.000 1.000
#> 57001     2  0.7299      0.753 0.204 0.796
#> 62001     2  0.5408      0.853 0.124 0.876
#> 62002     1  0.9710      0.324 0.600 0.400
#> 62003     1  0.0000      0.963 1.000 0.000
#> 63001     2  0.0000      0.954 0.000 1.000
#> 64001     2  0.0000      0.954 0.000 1.000
#> 64002     1  0.0000      0.963 1.000 0.000
#> 65005     2  0.0000      0.954 0.000 1.000
#> 68001     1  0.0000      0.963 1.000 0.000
#> 68003     1  0.9732      0.313 0.596 0.404
#> 84004     2  0.0000      0.954 0.000 1.000
#> LAL5      2  0.4161      0.890 0.084 0.916
#> 01003     2  0.8386      0.651 0.268 0.732
#> 01007     1  0.0000      0.963 1.000 0.000
#> 02020     1  0.0000      0.963 1.000 0.000
#> 04018     2  0.9795      0.306 0.416 0.584
#> 09002     2  0.0938      0.947 0.012 0.988
#> 10005     2  0.0000      0.954 0.000 1.000
#> 11002     2  0.0000      0.954 0.000 1.000
#> 12008     1  0.0000      0.963 1.000 0.000
#> 15006     1  0.0000      0.963 1.000 0.000
#> 16002     2  0.0000      0.954 0.000 1.000
#> 16007     2  0.0000      0.954 0.000 1.000
#> 17003     1  0.0000      0.963 1.000 0.000
#> 18001     2  0.0000      0.954 0.000 1.000
#> 19002     1  0.0000      0.963 1.000 0.000
#> 19008     2  0.0000      0.954 0.000 1.000
#> 19014     1  0.0000      0.963 1.000 0.000
#> 19017     2  0.0000      0.954 0.000 1.000
#> 20005     2  0.0000      0.954 0.000 1.000
#> 24006     1  0.0000      0.963 1.000 0.000
#> 26009     1  0.0000      0.963 1.000 0.000
#> 28008     2  0.0000      0.954 0.000 1.000
#> 28009     1  0.1184      0.949 0.984 0.016
#> 31015     2  0.0000      0.954 0.000 1.000
#> 37001     1  0.0000      0.963 1.000 0.000
#> 43006     2  0.0000      0.954 0.000 1.000
#> 43015     2  0.0000      0.954 0.000 1.000
#> 44001     2  0.6343      0.811 0.160 0.840
#> 49004     2  0.0000      0.954 0.000 1.000
#> 56007     2  0.5294      0.857 0.120 0.880
#> 64005     1  0.0000      0.963 1.000 0.000
#> 65003     1  0.6623      0.776 0.828 0.172
#> 83001     1  0.0000      0.963 1.000 0.000
#> LAL4      1  0.8955      0.543 0.688 0.312

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

consensus_heatmap(res, k = 2)

plot of chunk tab-ATC-NMF-consensus-heatmap-1

Heatmaps for the membership of samples in all partitions to see how consistent they are:

membership_heatmap(res, k = 2)

plot of chunk tab-ATC-NMF-membership-heatmap-1

As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.

Signature heatmaps where rows are scaled:

get_signatures(res, k = 2)

plot of chunk tab-ATC-NMF-get-signatures-1

Signature heatmaps where rows are not scaled:

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-ATC-NMF-get-signatures-no-scale-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-NMF-signature_compare

get_signature() returns a data frame invisibly. TO get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-ATC-NMF-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-NMF-collect-classes

Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.

test_to_known_factors(res)

#>           n sex(p) age(p)  BT(p) k
#> ATC:NMF 122  0.669 0.1273 0.5879 2
#> ATC:NMF 118  0.646 0.0450 0.6609 3
#> ATC:NMF  78  0.691 0.0518 0.2055 4
#> ATC:NMF  74  0.512 0.1193 0.0227 5
#> ATC:NMF  93  0.145 0.8612 0.0866 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

Session info

sessionInfo()

#> R version 3.6.0 (2019-04-26)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: CentOS Linux 7 (Core)
#> 
#> Matrix products: default
#> BLAS:   /usr/lib64/libblas.so.3.4.2
#> LAPACK: /usr/lib64/liblapack.so.3.4.2
#> 
#> locale:
#>  [1] LC_CTYPE=en_GB.UTF-8       LC_NUMERIC=C               LC_TIME=en_GB.UTF-8       
#>  [4] LC_COLLATE=en_GB.UTF-8     LC_MONETARY=en_GB.UTF-8    LC_MESSAGES=en_GB.UTF-8   
#>  [7] LC_PAPER=en_GB.UTF-8       LC_NAME=C                  LC_ADDRESS=C              
#> [10] LC_TELEPHONE=C             LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C       
#> 
#> attached base packages:
#> [1] grid      stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] genefilter_1.66.0    ComplexHeatmap_2.3.1 markdown_1.1         knitr_1.26          
#> [5] GetoptLong_0.1.7     cola_1.3.2          
#> 
#> loaded via a namespace (and not attached):
#>  [1] circlize_0.4.8       shape_1.4.4          xfun_0.11            slam_0.1-46         
#>  [5] lattice_0.20-38      splines_3.6.0        colorspace_1.4-1     vctrs_0.2.0         
#>  [9] stats4_3.6.0         blob_1.2.0           XML_3.98-1.20        survival_2.44-1.1   
#> [13] rlang_0.4.2          pillar_1.4.2         DBI_1.0.0            BiocGenerics_0.30.0 
#> [17] bit64_0.9-7          RColorBrewer_1.1-2   matrixStats_0.55.0   stringr_1.4.0       
#> [21] GlobalOptions_0.1.1  evaluate_0.14        memoise_1.1.0        Biobase_2.44.0      
#> [25] IRanges_2.18.3       parallel_3.6.0       AnnotationDbi_1.46.1 highr_0.8           
#> [29] Rcpp_1.0.3           xtable_1.8-4         backports_1.1.5      S4Vectors_0.22.1    
#> [33] annotate_1.62.0      skmeans_0.2-11       bit_1.1-14           microbenchmark_1.4-7
#> [37] brew_1.0-6           impute_1.58.0        rjson_0.2.20         png_0.1-7           
#> [41] digest_0.6.23        stringi_1.4.3        polyclip_1.10-0      clue_0.3-57         
#> [45] tools_3.6.0          bitops_1.0-6         magrittr_1.5         eulerr_6.0.0        
#> [49] RCurl_1.95-4.12      RSQLite_2.1.4        tibble_2.1.3         cluster_2.1.0       
#> [53] crayon_1.3.4         pkgconfig_2.0.3      zeallot_0.1.0        Matrix_1.2-17       
#> [57] xml2_1.2.2           httr_1.4.1           R6_2.4.1             mclust_5.4.5        
#> [61] compiler_3.6.0